Anatole Katok - Author Profile

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Katok, Anatole (b. 1944 d. 2018)

Author ID:	katok.anatole
Published as:	Katok, Anatole; Katok, A.; Katok, A. B.; Katok, Anatole B.; Katok, Anatoly more...less
Further Spellings:	Katok, Anatoliĭ Borisovich; Каток Анатолий Борисович
External Links:	MGP · Wikidata · Google Scholar · Math-Net.Ru · GND · IdRef

Documents Indexed:	132 Publications since 1964, including 11 Books and 1 Additional arXiv Preprint
	7 Contributions as Editor
Biographic References:	8 Publications
Co-Authors:	82 Co-Authors with 103 Joint Publications
	2,877 Co-Co-Authors

all top 5

Co-Authors

35	single-authored
13	Rodriguez-Hertz, Federico
9	Hasselblatt, Boris
7	Katok, Svetlana R.
7	Spatzier, Ralf J.
6	Damjanović, Danijela
6	Kalinin, Boris
6	Stëpin, Anatoliĭ Mikhaĭlovich
5	Anosov, Dmitriĭ Viktorovich
5	Fayad, Bassam R.
5	Pesin, Yakov Borisovich
4	Weiss, Howard
4	Zemlyakov, A. N.
3	Climenhaga, Vaughn
3	Einsiedler, Manfred Leopold
3	Feres, Renato
3	Hurder, Steven E.
3	Knieper, Gerhard
3	Lemańczyk, Mariusz
3	Lewis, James Welsh
3	Niţică, Viorel
3	Sinaĭ, Yakov Grigor’evich
2	Brin, Michael
2	Burns, Keith
2	Forni, Giovanni
2	Grines, Vyacheslav Zigmundovich
2	Gutkin, Eugene
2	Kozlov, Valeriĭ Vasil’evich
2	Neĭshtadt, Anatoliĭ Iserovich
2	Pollicott, Mark
2	Przytycki, Feliks
2	Schmidt, Klaus
2	Thouvenot, Jean-Paul
1	Afraimovich, Valentin S.
1	Aseev, Sergei M.
1	Bernstein, David
1	Bochi, Jairo
1	Bolibrukh, Andreĭ Andreevich
1	Bukhshtaber, Viktor Matveevich
1	Bunimovich, Leonid Abramovich
1	Davydov, Alekseĭ Aleksandrovich
1	de la Llave, Rafael
1	Erchenko, Alena
1	Feldman, Jacob
1	Flaminio, Livio
1	Foiaș, Ciprian
1	Gerber, Marlies
1	Gonchenko, Sergeĭ Vladimirovich
1	Grigorchuk, Rostislav Ivanovich
1	Gunesch, Roland
1	Gurevich, Boris
1	Il’yashenko, Yuliĭ Sergeevich
1	Kanigowski, Adam
1	Kashchenko, Sergeĭ Aleksandrovich
1	Kifer, Yuri
1	Klimenko, Alexey V.
1	Kononenko, Alexey
1	Krikorian, Raphaël
1	Kulikov, M. S.
1	Ledrappier, François
1	Leksin, Vladimir Pavlovich
1	Lerman, Lev
1	Lindenstrauss, Elon
1	Mezhirov, A. M.
1	Monastyrskiĭ, Mikhail Il’ich
1	Morozov, Al’bert Dmitrievich
1	Novikov, Sergeĭ Petrovich
1	Prikhod’ko, Aleksandr A.
1	Robinson, E. Arthur jun.
1	Samoĭlenko, Anatoliĭ Mykhaĭlovych
1	Sataev, A. B.
1	Sataev, Evgueni A.
1	Sharkovs’kyĭ, Oleksandr Mykolaĭovych
1	Shilnikov, Andrey L.
1	Strelcyn, Jean-Marie
1	Török, Andrei
1	Treshchev, Dmitriĭ Valer’evich
1	Turaev, Dmitry V.
1	Wei, Daren
1	Windsor, Alistair
1	Zakalyukin, Vladimir M.
1	Zelikin, Mikhail Il’ich
1	Zhirov, Aleksei Yu.
1	Zhuzhoma, Evgeniĭ Viktorovich
1	Zimmer, Robert J.

all top 5

Serials

18	Ergodic Theory and Dynamical Systems
7	Journal of Modern Dynamics
6	Uspekhi Matematicheskikh Nauk [N. S.]
6	Annals of Mathematics. Second Series
5	Israel Journal of Mathematics
5	Discrete and Continuous Dynamical Systems
3	Communications in Mathematical Physics
3	Mathematical Notes
3	Russian Mathematical Surveys
3	Fundamenta Mathematicae
3	Publications Mathématiques
3	Inventiones Mathematicae
3	Soviet Mathematics. Doklady
3	Mathematical Research Letters
2	Matematicheskie Zametki
2	Commentarii Mathematici Helvetici
2	Funktsional’nyĭ Analiz i ego Prilozheniya
2	Mathematics of the USSR. Izvestiya
2	Bulletin of the American Mathematical Society. New Series
2	Electronic Research Announcements of the American Mathematical Society
2	Encyclopedia of Mathematics and Its Applications
2	Progress in Mathematics
2	Student Mathematical Library
1	Communications on Pure and Applied Mathematics
1	Journal d’Analyse Mathématique
1	Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1	Geometriae Dedicata
1	Journal of Soviet Mathematics
1	Pacific Journal of Mathematics
1	Topology
1	Transactions of the Moscow Mathematical Society
1	Trudy Moskovskogo Matematicheskogo Obshchestva
1	IMRN. International Mathematics Research Notices
1	Geometric and Functional Analysis. GAFA
1	Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
1	Notices of the American Mathematical Society
1	Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1	Journal of Dynamical and Control Systems
1	Moscow Mathematical Journal
1	Comptes Rendus. Mathématique. Académie des Sciences, Paris
1	Cambridge Tracts in Mathematics
1	Contemporary Mathematics
1	Lecture Notes in Mathematics
1	Proceedings of Symposia in Pure Mathematics
1	Translations. Series 2. American Mathematical Society
1	University Lecture Series
1	Electronic Research Announcements in Mathematical Sciences

all top 5

Fields

110	Dynamical systems and ergodic theory (37-XX)
36	Measure and integration (28-XX)
17	Manifolds and cell complexes (57-XX)
13	Differential geometry (53-XX)
11	History and biography (01-XX)
10	Topological groups, Lie groups (22-XX)
10	General topology (54-XX)
8	General and overarching topics; collections (00-XX)
7	Global analysis, analysis on manifolds (58-XX)
4	Operator theory (47-XX)
3	Geometry (51-XX)
3	Mechanics of particles and systems (70-XX)
2	Ordinary differential equations (34-XX)
2	Harmonic analysis on Euclidean spaces (42-XX)
2	Probability theory and stochastic processes (60-XX)
1	Number theory (11-XX)
1	Group theory and generalizations (20-XX)
1	Several complex variables and analytic spaces (32-XX)
1	Partial differential equations (35-XX)
1	Functional analysis (46-XX)
1	Calculus of variations and optimal control; optimization (49-XX)
1	Numerical analysis (65-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

124 Publications have been cited 5,160 times in 3,642 Documents	Cited by ▼	Year ▼
Introduction to the modern theory of dynamical systems. Zbl 0878.58020 Katok, Anatole; Hasselblatt, Boris	1,576	1995
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Zbl 0445.58015 Katok, A.	483	1980
On local entropy. Zbl 0533.58020 Brin, M.; Katok, A.	172	1983
Introduction to the modern theory of dynamical systems. With a supplement by Anatole Katok and Leonardo Mendoza. Zbl 0878.58019 Katok, Anatole; Hasselblatt, Boris	151	1997
Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki. Zbl 0658.58001 Katok, Anatole; Strelcyn, Jean-Marie	118	1986
A first course in dynamics with a panorama of recent developments. Zbl 1027.37001 Hasselblatt, Boris; Katok, Anatole	104	2003
Ergodic perturbations of degenerate integrable Hamiltonian systems. Zbl 0316.58010 Katok, A. B.	94	1974
Approximations in ergodic theory. Zbl 0172.07202 Katok, A. B.; Stepin, A. M.	91	1967
Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004 Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon	78	2006
Bernoulli diffeomorphisms on surfaces. Zbl 0435.58021 Katok, A.	72	1979
Constructions in elliptic dynamics. Zbl 1089.37012 Fayad, Bassam; Katok, Anatole	70	2004
Entropy and closed geodesics. Zbl 0525.58027 Katok, A.	63	1982
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034 Hurder, S.; Katok, A.	63	1990
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027 Katok, Anatole; Spatzier, Ralf J.	60	1994
Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021 Katok, A.; Spatzier, R. J.	58	1996
Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009 Katok, Anatole	57	1980
Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001 Katok, Anatole	54	2003
Handbook of dynamical systems. Volume 1A. Zbl 1013.00016	53	2002
New examples in smooth ergodic theory. Ergodic diffeomorphisms. Zbl 0255.58007 Anosov, D. V.; Katok, A. B.	51	1972
Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009 Katok, Anatole; Thouvenot, Jean-Paul	51	1997
Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053 Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.	50	1989
Manifolds with non-positive curvature. Zbl 0572.58019 Burns, K.; Katok, A.	50	1985
Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010 Katok, A.; Spatzier, R. J.	49	1997
Topological transitivity of billiards in polygons. Zbl 0323.58012 Zemlyakov, A. N.; Katok, A. B.	47	1976
Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001 Katok, Anatole	47	2007
Topologische Transitivität von Billards in Polygonen. Zbl 0315.58014 Zemlyakov, A. N.; Katok, A. B.	44	1975
Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048 Katok, A.	43	1982
Neue Beispiele in der differenzierbaren Ergodentheorie. Ergodische Diffeomorphismen. Zbl 0218.58008 Anosov, D. V.; Katok, A. B.	43	1970
Cocycles, cohomology and combinatorial constructions in ergodic theory. Zbl 0994.37003 Katok, Anatole; Robinson, E. A. jun.	40	2001
Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042 Katok, Anatole	40	1988
Invariant measures of flows on oriented surfaces. Zbl 0298.28013 Katok, A. B.	39	1973
Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040 Bernstein, David; Katok, Anatole	39	1987
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029 Katok, Anatole; Burns, Keith	38	1994
Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012 Katok, A.; Lewis, J.	36	1991
Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003 Katok, Anatole; Nitică, Viorel	34	2011
Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus. Zbl 1209.37017 Damjanović, Danijela; Katok, Anatole	33	2010
Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082 Katok, A.; Kononenko, A.	33	1996
Caustics for inner and outer billiards. Zbl 0839.58036 Gutkin, Eugene; Katok, Anatole	31	1995
The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020 Katok, A.	31	1987
Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304 Katok, Anatole; Thouvenot, Jean-Paul	27	2006
Principal structures. Zbl 1047.37001 Hasselblatt, Boris; Katok, Anatole	26	2002
Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus. Zbl 1035.37005 Katok, Anatole; Katok, Svetlana; Schmidt, Klaus	26	2002
Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations. Zbl 0988.37063 Guysinsky, M.; Katok, A.	25	1998
Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Zbl 0857.57038 Katok, A.; Lewis, J.	24	1996
Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016 Kalinin, Boris; Katok, Anatole	24	2001
Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026 Katok, A.; Spatzier, R. J.	23	1994
Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Zbl 0749.58041 Katok, Anatole; Knieper, Gerhard; Weiss, Howard	22	1991
Invariant measures on \(G/{\Gamma}\) for split simple Lie groups \(G\). Zbl 1022.22023 Einsiedler, Manfred; Katok, Anatole	20	2003
Nonuniform measure rigidity. Zbl 1368.37031 Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez	19	2011
Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017 Einsiedler, Manfred; Katok, Anatole	19	2005
Theory of dynamical systems and general transformation groups with invariant measure. Zbl 0399.28011 Katok, A. B.; Sinai, Ya. G.; Stepin, A. M.	19	1975
Random perturbations of transformations of an interval. Zbl 0616.60064 Katok, A.; Kifer, Y.	19	1986
Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016 Katok, Anatole	19	1984
Monotone equivalence in ergodic theory. Zbl 0379.28008 Katok, A. B.	18	1977
Smooth non-Bernoulli k-automorphisms. Zbl 0467.58016 Katok, A.	17	1980
Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037 Katok, A.; Lewis, J.; Zimmer, R.	17	1996
Ergodic theory and Weil measures for foliations. Zbl 0645.57021 Hurder, S.; Katok, A.	17	1987
Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026 Damjanovic, Danijela; Katok, Anatole	17	2011
Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions. Zbl 1109.37029 Damjanović, Danijela; Katok, Anatole	16	2005
Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039 Katok, Anatole; Katok, Svetlana	16	1995
Local rigidity of partially hyperbolic actions. II: The geometric method and restrictions of Weyl chamber flows on \(\mathrm{SL}(n,\mathbb R)/\Gamma \). Zbl 1291.37027 Damjanović, Danijela; Katok, Anatole	14	2011
Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021 Brin, M. I.; Feldman, J.; Katok, A.	14	1981
Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017 Kalinin, Boris; Katok, Anatole	14	2007
Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029 Gerber, Marlies; Katok, Anatole	13	1982
Monotone Äquivalenz in der Ergodentheorie. Zbl 0372.28020 Katok, A. B.	13	1977
Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023 Katok, Anatole; Katok, Svetlana	12	2005
Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032 Katok, A.	12	1983
Approximation of ergodic dynamical systems by periodic transformations. Zbl 0186.46701 Katok, A. B.; Stepin, A. M.	12	1966
Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042 Katok, Anatole; Niţică, Viorel; Török, Andrei	12	2000
Handbook of dynamical systems. Volume 1B. Zbl 1081.00006	12	2006
Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083 Erchenko, Alena; Katok, Anatole	12	2019
Metric properties of measure preserving homeomorphisms. Zbl 0209.27803 Katok, A. B.; Stepin, A. M.	11	1970
Ergodic theory and dynamics of \(G\)-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029 Feres, Renato; Katok, Anatole	11	2002
The Fried average entropy and slow entropy for actions of higher rank abelian groups. Zbl 1308.37005 Katok, Anatole; Katok, Svetlana; Rodriguez Hertz, Federico	10	2014
Metric properties of homeomorphisms which preserve the measure. Zbl 0198.55701 Katok, A. B.; Stepin, A. M.	10	1970
Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure. With an appendix by Alex Furman. Zbl 1009.37013 Gunesch, Roland; Katok, Anatole B.	10	2000
Some new cases of realization of spectral multiplicity function for ergodic transformations. Zbl 1187.37005 Katok, A.; Lemańczyk, M.	10	2009
Mixed spectrum reparameterizations of linear flows on \(\mathbb T^2\). Zbl 1123.37300 Fayad, Bassam; Katok, Anatole; Windsor, Alistar	10	2001
Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050 Feres, Renato; Katok, Anatoly	10	1989
Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021 Fayad, Bassam; Katok, Anatole	9	2014
Anasov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature. Zbl 0729.58039 Feres, Renato; Katok, Anatole	9	1990
Lectures on surfaces. (Almost) everything you wanted to know about them. Zbl 1169.53001 Katok, Anatole; Climenhaga, Vaughn	9	2008
Standardness of automorphisms of transposition of intervals and fluxes on surfaces. Zbl 0368.58010 Katok, A. B.; Sataev, A. B.	9	1976
Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037 Katok, Anatole; Hertz, Federico Rodriguez	8	2010
Neue Beispiele ergodischer Diffeomorphismen glatter Mannigfaltigkeiten. Zbl 0203.56502 Anosov, D. V.; Katok, A. B.	8	1970
The cohomology of expansive \(\mathbb{Z}^ d\)-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015 Katok, Anatole B.; Schmidt, Klaus	8	1995
Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024 Katok, A.	8	1992
Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045 Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.	8	1990
Time change, monotone equivalent and standard dynamical systems. Zbl 0326.28025 Katok, A. B.	7	1975
Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015 Hurder, S.; Katok, A.	7	1984
A conjecture about entropy. Zbl 0628.58026 Katok, A. B.	7	1977
Spectral properties of dynamical systems with an integral invariant on the torus. Zbl 0172.12102 Katok, A. B.	7	1967
Flexibility of Lyapunov exponents. Zbl 1495.37024 Bochi, J.; Katok, A.; Rodriguez Hertz, F.	7	2022
Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048 Katok, Anatole; Rodriguez Hertz, Federico	7	2016
Measurable rigidity and disjointness for \(\mathbb Z^ k\) actions by toral automorphisms. Zbl 1056.37029 Kalinin, Boris; Katok, Anatole	6	2002
Local rigidity of actions of higher rank abelian groups and KAM method. Zbl 1068.37015 Damjanović, Danijela; Katok, Anatole	5	2004
Billiard table as a playground for a mathematician. Zbl 1147.37329 Katok, A. B.	5	2005
Hyperbolic measures and commuting maps in low dimension. Zbl 0948.37002 Katok, Anatole	5	1996
Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups. Zbl 1120.37017 Katok, A.; Niţică, V.	5	2007
Dynamical systems with hyperbolic structure. Zbl 0598.58031 Katok, A. B.	5	1981
Flexibility of Lyapunov exponents. Zbl 1495.37024 Bochi, J.; Katok, A.; Rodriguez Hertz, F.	7	2022
Flexibility of entropies for surfaces of negative curvature. Zbl 1421.53083 Erchenko, Alena; Katok, Anatole	12	2019
Modern theory of dynamical systems. A tribute to Dmitry Victorovich Anosov. Zbl 1370.37002	5	2017
From groups to geometry and back. Zbl 1428.20001 Climenhaga, Vaughn; Katok, Anatole	4	2017
Dmitry Viktorovich Anosov: his life and mathematics. Zbl 1386.01011 Katok, Anatole	2	2017
Non-uniform measure rigidity for \(\mathbb{Z}^k\) actions of symplectic type. Zbl 1388.37032 Katok, Anatole; Rodriguez Hertz, Federico	1	2017
Arithmeticity and topology of smooth actions of higher rank abelian groups. Zbl 1370.37048 Katok, Anatole; Rodriguez Hertz, Federico	7	2016
The Fried average entropy and slow entropy for actions of higher rank abelian groups. Zbl 1308.37005 Katok, Anatole; Katok, Svetlana; Rodriguez Hertz, Federico	10	2014
Analytic uniquely ergodic volume preserving maps on odd spheres. Zbl 1336.37021 Fayad, Bassam; Katok, Anatole	9	2014
Rigidity in higher rank abelian group actions. Volume 1. Introduction and cocycle problem. Zbl 1232.37003 Katok, Anatole; Nitică, Viorel	34	2011
Nonuniform measure rigidity. Zbl 1368.37031 Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez	19	2011
Local rigidity of homogeneous parabolic actions: I. A model case. Zbl 1284.37026 Damjanovic, Danijela; Katok, Anatole	17	2011
Local rigidity of partially hyperbolic actions. II: The geometric method and restrictions of Weyl chamber flows on \(\mathrm{SL}(n,\mathbb R)/\Gamma \). Zbl 1291.37027 Damjanović, Danijela; Katok, Anatole	14	2011
Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus. Zbl 1209.37017 Damjanović, Danijela; Katok, Anatole	33	2010
Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank Abelian groups. Zbl 1213.37037 Katok, Anatole; Hertz, Federico Rodriguez	8	2010
Rigidity of real-analytic actions of \(SL(n,\mathbb Z)\) on \(\mathbb T^n\): a case of realization of Zimmer program. Zbl 1192.37025 Katok, Anatole; Hertz, Federico Rodriguez	5	2010
Errata to “Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on Tori” and “Uniqueness of large invariant measures for \(\mathbb Z^k\) actions with Cartan homotopy data”. Zbl 1192.37026 Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez	3	2010
Some new cases of realization of spectral multiplicity function for ergodic transformations. Zbl 1187.37005 Katok, A.; Lemańczyk, M.	10	2009
Lectures on surfaces. (Almost) everything you wanted to know about them. Zbl 1169.53001 Katok, Anatole; Climenhaga, Vaughn	9	2008
New progress in nonuniform measure and cocycle rigidity. Zbl 1159.37316 Kalinin, Boris; Katok, Anatole; Hertz, Federico Rodriguez	4	2008
Moscow dynamics seminars of the nineteen seventies and the early career of Yasha Pesin. Zbl 1152.01009 Katok, Anatole	3	2008
Fifty years of entropy in dynamics: 1958 – 2007. Zbl 1149.37001 Katok, Anatole	47	2007
Measure rigidity beyond uniform hyperbolicity: invariant measures for Cartan actions on tori. Zbl 1173.37017 Kalinin, Boris; Katok, Anatole	14	2007
Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups. Zbl 1120.37017 Katok, A.; Niţică, V.	5	2007
Uniqueness of large invariant measures for \(\mathbb Z^k\) actions with Cartan homotopy data. Zbl 1136.37016 Katok, Anatole; Rodriguez Hertz, Federico	5	2007
Local rigidity of restrictions of Weyl chamber flows. Zbl 1113.37015 Damjanović, Danijela; Katok, Anatole	3	2007
Invariant measures and the set of exceptions to Littlewood’s conjecture. Zbl 1109.22004 Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon	78	2006
Spectral properties and combinatorial constructions in ergodic theory. Zbl 1130.37304 Katok, Anatole; Thouvenot, Jean-Paul	27	2006
Handbook of dynamical systems. Volume 1B. Zbl 1081.00006	12	2006
Rigidity of measures – the high entropy case and non-commuting foliations. Zbl 1097.37017 Einsiedler, Manfred; Katok, Anatole	19	2005
Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions. Zbl 1109.37029 Damjanović, Danijela; Katok, Anatole	16	2005
Higher cohomology for abelian groups of toral automorphisms. II: The partially hyperbolic case and corrigendum. Zbl 1109.57023 Katok, Anatole; Katok, Svetlana	12	2005
Billiard table as a playground for a mathematician. Zbl 1147.37329 Katok, A. B.	5	2005
Constructions in elliptic dynamics. Zbl 1089.37012 Fayad, Bassam; Katok, Anatole	70	2004
Local rigidity of actions of higher rank abelian groups and KAM method. Zbl 1068.37015 Damjanović, Danijela; Katok, Anatole	5	2004
A first course in dynamics with a panorama of recent developments. Zbl 1027.37001 Hasselblatt, Boris; Katok, Anatole	104	2003
Combinatorial constructions in ergodic theory and dynamics. Zbl 1030.37001 Katok, Anatole	54	2003
Invariant measures on \(G/{\Gamma}\) for split simple Lie groups \(G\). Zbl 1022.22023 Einsiedler, Manfred; Katok, Anatole	20	2003
Handbook of dynamical systems. Volume 1A. Zbl 1013.00016	53	2002
Principal structures. Zbl 1047.37001 Hasselblatt, Boris; Katok, Anatole	26	2002
Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus. Zbl 1035.37005 Katok, Anatole; Katok, Svetlana; Schmidt, Klaus	26	2002
Ergodic theory and dynamics of \(G\)-spaces (with special emphasis on rigidity phenomena). Zbl 1055.37029 Feres, Renato; Katok, Anatole	11	2002
Measurable rigidity and disjointness for \(\mathbb Z^ k\) actions by toral automorphisms. Zbl 1056.37029 Kalinin, Boris; Katok, Anatole	6	2002
The development of dynamics in the 20th century and the contribution of Jürgen Moser. Zbl 1018.37001 Hasselblatt, Boris; Katok, Anatole	2	2002
Cocycles, cohomology and combinatorial constructions in ergodic theory. Zbl 0994.37003 Katok, Anatole; Robinson, E. A. jun.	40	2001
Invariant measures for actions of higher rank abelian groups. Zbl 0999.37016 Kalinin, Boris; Katok, Anatole	24	2001
Mixed spectrum reparameterizations of linear flows on \(\mathbb T^2\). Zbl 1123.37300 Fayad, Bassam; Katok, Anatole; Windsor, Alistar	10	2001
Smooth ergodic theory and its applications. Proceedings of the AMS summer research institute, Seattle, WA, USA, July 26–August 13, 1999. Zbl 0973.00044	3	2001
Non-abelian cohomology of abelian Anosov actions. Zbl 0977.57042 Katok, Anatole; Niţică, Viorel; Török, Andrei	12	2000
Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure. With an appendix by Alex Furman. Zbl 1009.37013 Gunesch, Roland; Katok, Anatole B.	10	2000
Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations. Zbl 0988.37063 Guysinsky, M.; Katok, A.	25	1998
Entropy and growth of expanding periodic orbits for one-dimensional maps. Zbl 0915.58025 Katok, A.; Mezhirov, A.	1	1998
Introduction to the modern theory of dynamical systems. With a supplement by Anatole Katok and Leonardo Mendoza. Zbl 0878.58019 Katok, Anatole; Hasselblatt, Boris	151	1997
Slow entropy type invariants and smooth realization of commuting measure-preserving transformations. Zbl 0884.60009 Katok, Anatole; Thouvenot, Jean-Paul	51	1997
Differential rigidity of Anosov actions of higher rank Abelian groups and algebraic lattice actions. Zbl 0938.37010 Katok, A.; Spatzier, R. J.	49	1997
Invariant measures for higher-rank hyperbolic abelian actions. Zbl 0859.58021 Katok, A.; Spatzier, R. J.	58	1996
Cocycles’ stability for partially hyperbolic systems. Zbl 0853.58082 Katok, A.; Kononenko, A.	33	1996
Global rigidity results for lattice actions on tori and new examples of volume-preserving actions. Zbl 0857.57038 Katok, A.; Lewis, J.	24	1996
Cocycle superrigidity and rigidity for lattice actions on tori. Zbl 0857.57037 Katok, A.; Lewis, J.; Zimmer, R.	17	1996
Hyperbolic measures and commuting maps in low dimension. Zbl 0948.37002 Katok, Anatole	5	1996
Nonstationary normal forms and rigidity of group actions. Zbl 0871.58073 Katok, A.; Spatzier, R. J.	3	1996
Introduction to the modern theory of dynamical systems. Zbl 0878.58020 Katok, Anatole; Hasselblatt, Boris	1,576	1995
Caustics for inner and outer billiards. Zbl 0839.58036 Gutkin, Eugene; Katok, Anatole	31	1995
Higher cohomology for Abelian groups of toral automorphisms. Zbl 0851.57039 Katok, Anatole; Katok, Svetlana	16	1995
The cohomology of expansive \(\mathbb{Z}^ d\)-actions by automorphisms of compact, Abelian groups. Zbl 0866.28015 Katok, Anatole B.; Schmidt, Klaus	8	1995
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity. Zbl 0819.58027 Katok, Anatole; Spatzier, Ralf J.	60	1994
Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dynamical systems. Zbl 0816.58029 Katok, Anatole; Burns, Keith	38	1994
Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions. Zbl 0836.57026 Katok, A.; Spatzier, R. J.	23	1994
Women in Soviet mathematics. Zbl 1194.01176 Katok, Anatole; Katok, Svetlana	3	1993
Minimal orbits for small perturbations of completely integrable Hamiltonian systems. Zbl 0762.58024 Katok, A.	8	1992
Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori. Zbl 0725.58033 Flaminio, L.; Katok, A.	5	1992
Local rigidity for certain groups of toral automorphisms. Zbl 0785.22012 Katok, A.; Lewis, J.	36	1991
Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Zbl 0749.58041 Katok, Anatole; Knieper, Gerhard; Weiss, Howard	22	1991
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Zbl 0725.58034 Hurder, S.; Katok, A.	63	1990
Anasov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature. Zbl 0729.58039 Feres, Renato; Katok, Anatole	9	1990
Differentiability of entropy for Anosov and geodesic flows. Zbl 0717.58045 Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.	8	1990
Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Zbl 0702.58053 Katok, A.; Knieper, G.; Pollicott, M.; Weiss, H.	50	1989
Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Zbl 0667.58050 Feres, Renato; Katok, Anatoly	10	1989
Vladimir Abramovich Rokhlin (23 August 1919 to 3 December 1984): Introductory note. Zbl 0688.01012 Katok, A.	2	1989
Four applications of conformal equivalence to geometry and dynamics. Zbl 0668.58042 Katok, Anatole	40	1988
Weakly mixing billiards. Zbl 0673.58028 Gutkin, E.; Katok, A.	5	1988
Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonian. Zbl 0642.58040 Bernstein, David; Katok, Anatole	39	1987
The growth rate for the number of singular and periodic orbits for a polygonal billiard. Zbl 0631.58020 Katok, A.	31	1987
Ergodic theory and Weil measures for foliations. Zbl 0645.57021 Hurder, S.; Katok, A.	17	1987
Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki. Zbl 0658.58001 Katok, Anatole; Strelcyn, Jean-Marie	118	1986
Random perturbations of transformations of an interval. Zbl 0616.60064 Katok, A.; Kifer, Y.	19	1986
Manifolds with non-positive curvature. Zbl 0572.58019 Burns, K.; Katok, A.	50	1985
Nonuniform hyperbolicity and structure of smooth dynamical systems. Zbl 0563.58016 Katok, Anatole	19	1984
Secondary classes and transverse measure theory of a foliation. Zbl 0593.58015 Hurder, S.; Katok, A.	7	1984
On local entropy. Zbl 0533.58020 Brin, M.; Katok, A.	172	1983
Periodic and quasi-periodic orbits for twist maps. Zbl 0517.58032 Katok, A.	12	1983
Entropy and closed geodesics. Zbl 0525.58027 Katok, A.	63	1982
Some remarks on Birkhoff and Mather twist map theorems. Zbl 0521.58048 Katok, A.	43	1982
Smooth models of Thurston’s pseudo-Anosov maps. Zbl 0502.58029 Gerber, Marlies; Katok, Anatole	13	1982
Ergodic theory and dynamical systems II. Proceedings, special year, Maryland 1979-80. Zbl 0483.00005	2	1982
Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents. Zbl 0477.58021 Brin, M. I.; Feldman, J.; Katok, A.	14	1981
Dynamical systems with hyperbolic structure. Zbl 0598.58031 Katok, A. B.	5	1981
Ergodic theory and dynamical systems I. Proceedings, Special Year, Maryland 1979-80. Zbl 0451.00006	2	1981
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Zbl 0445.58015 Katok, A.	483	1980
Interval exchange transformations and some special flows are not mixing. Zbl 0437.28009 Katok, Anatole	57	1980
...and 24 more Documents

all cited Publications top 5 cited Publications

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Cited by 3,145 Authors

36	Katok, Anatole
29	Morales Rojas, Carlos Arnoldo
26	Varandas, Paulo
25	Barreira, Luis Manuel
24	de la Llave, Rafael
24	Pesin, Yakov Borisovich
23	Rodriguez-Hertz, Federico
22	Chen, Ercai
22	Troubetzkoy, Serge Eugene
21	Einsiedler, Manfred Leopold
21	Huang, Wen
20	Gelfert, Katrin Grit
20	Lindenstrauss, Elon
20	Sun, Wenxiang
19	Fayad, Bassam R.
19	Kanigowski, Adam
19	Pollicott, Mark
19	Zhao, Yun
18	Cao, Yongluo
18	Kuznetsov, Sergey P.
18	Valls Anglés, Cláudia
17	Forni, Giovanni
17	Kalinin, Boris
17	Lemańczyk, Mariusz
17	Sadovskaya, Victoria
17	Tian, Xueting
16	Oertel-Jäger, Tobias Hendrik
16	Kunde, Philipp
16	Mesón, Alejandro M.
16	Vericat, Fernando
16	Yang, Jiagang
16	Young, Lai-Sang
15	Buzzi, Jérôme
15	Climenhaga, Vaughn
15	Damjanović, Danijela
15	Frączek, Krzysztof Marek
15	Kolesov, Andreĭ Yur’evich
15	Ledrappier, François
15	Paternain, Gabriel Pedro
14	Baladi, Viviane
14	Glyzin, Sergeĭ Dmitrievich
14	Gogolev, Andrey
14	Gutkin, Eugene
14	Hasselblatt, Boris
14	Ryzhikov, Valeriĭ Valentinovich
14	Spatzier, Ralf J.
13	Avila, Artur
13	Chaika, Jonathan
13	Crovisier, Sylvain
13	Dolgopyat, Dmitry
13	Dragičević, Davor
13	Duan, Huagui
13	Knieper, Gerhard
13	Stoyanov, Luchezar N.
13	Zhu, Yujun
12	Bonatti, Christian
12	Bunimovich, Leonid Abramovich
12	Grines, Vyacheslav Zigmundovich
12	Li, Zhiming
12	Ulcigrai, Corinna
12	Vetokhin, Alexandr N.
12	Xu, Leiye
12	Zhou, Yunhua
11	Araújo, Vítor
11	Cheng, Wenchiao
11	Ferenczi, Sébastien
11	Ginzburg, Viktor L’vovich
11	Guillarmou, Colin
11	Gürel, Basak Zehra
11	Le Calvez, Patrice
11	Lefeuvre, Thibault
11	Liu, Hui
11	Long, Yiming
11	Qin, Wenxin
11	Tien Cuong Dinh
11	Wilkinson, Amie
11	Ye, Xiangdong
10	Bessa, Mário
10	Chernov, Nikolai Ivanovich
10	Giona, Massimiliano
10	Gorodetskii, Anton Semenovich
10	Kawan, Christoph
10	Liu, Lei
10	Llibre, Jaume
10	Masur, Howard A.
10	Potrie, Rafael
10	Shu, Lin
10	Viana, Marcelo
10	Wang, Wei
10	Wang, Zhenqi Jenny
10	Weiss, Howard
10	Wu, Weisheng
10	Zhou, Xiaoyao
9	Alves, Marcelo R. R.
9	Backes, Lucas H.
9	Boyland, Philip L.
9	Burns, Keith
9	Damanik, David
9	de Thélin, Henry
9	Del Magno, Gianluigi
...and 3,045 more Authors

all top 5

Cited in 426 Serials

287	Ergodic Theory and Dynamical Systems
124	Discrete and Continuous Dynamical Systems
123	Communications in Mathematical Physics
102	Transactions of the American Mathematical Society
101	Israel Journal of Mathematics
91	Proceedings of the American Mathematical Society
90	Journal of Differential Equations
85	Physica D
83	Nonlinearity
82	Journal of Statistical Physics
76	Advances in Mathematics
73	Inventiones Mathematicae
61	Journal of Modern Dynamics
54	Journal of Mathematical Analysis and Applications
54	Dynamical Systems
50	Annales de l’Institut Fourier
45	Duke Mathematical Journal
43	Journal of Dynamics and Differential Equations
38	Mathematische Zeitschrift
36	Mathematical Notes
35	Chaos
35	Annals of Mathematics. Second Series
33	Journal d’Analyse Mathématique
33	Mathematische Annalen
32	Chaos, Solitons and Fractals
32	Qualitative Theory of Dynamical Systems
31	Geometriae Dedicata
31	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
31	Regular and Chaotic Dynamics
30	Topology and its Applications
28	Geometric and Functional Analysis. GAFA
28	Journal of Mathematical Sciences (New York)
27	Journal of Dynamical and Control Systems
26	SIAM Journal on Applied Dynamical Systems
25	Journal of the European Mathematical Society (JEMS)
24	Bulletin of the American Mathematical Society. New Series
24	Acta Mathematica Sinica. English Series
23	Geometry & Topology
21	Functional Analysis and its Applications
21	Journal of Functional Analysis
21	Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
21	Journal of the American Mathematical Society
20	Stochastics and Dynamics
20	Proceedings of the Steklov Institute of Mathematics
19	Commentarii Mathematici Helvetici
19	Monatshefte für Mathematik
19	Comptes Rendus. Mathématique. Académie des Sciences, Paris
18	Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
18	Journal of Difference Equations and Applications
17	Physics Letters. A
17	Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
16	Annales Henri Poincaré
16	Bulletin of the Brazilian Mathematical Society. New Series
15	Bulletin de la Société Mathématique de France
14	Communications in Nonlinear Science and Numerical Simulation
13	Journal of Fixed Point Theory and Applications
13	Science China. Mathematics
12	Mathematical Proceedings of the Cambridge Philosophical Society
12	Journal of Geometry and Physics
12	Publications Mathématiques
12	Journal of Nonlinear Science
12	Calculus of Variations and Partial Differential Equations
12	Discrete and Continuous Dynamical Systems. Series B
12	Journal de l’École Polytechnique – Mathématiques
11	Journal of the London Mathematical Society. Second Series
11	Differential Equations
10	Journal of Mathematical Physics
10	The Journal of Geometric Analysis
10	Electronic Research Announcements of the American Mathematical Society
9	Bulletin of the London Mathematical Society
9	Compositio Mathematica
9	Memoirs of the American Mathematical Society
9	Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
8	Russian Mathematical Surveys
8	Theoretical Computer Science
8	Systems & Control Letters
8	Differential Geometry and its Applications
8	Journal of Dynamical Systems and Geometric Theories
8	Journal of the Institute of Mathematics of Jussieu
8	Journal of Topology and Analysis
7	Automatica
7	Experimental Mathematics
7	Conformal Geometry and Dynamics
7	Arnold Mathematical Journal
7	Annales Henri Lebesgue
6	Archive for Rational Mechanics and Analysis
6	Moscow University Mathematics Bulletin
6	Fundamenta Mathematicae
6	Indiana University Mathematics Journal
6	Journal de Mathématiques Pures et Appliquées. Neuvième Série
6	Proceedings of the Indian Academy of Sciences. Mathematical Sciences
6	Annales de l’Institut Henri Poincaré. Physique Théorique
6	Sbornik: Mathematics
6	Algebraic & Geometric Topology
6	Acta Mathematica Scientia. Series B. (English Edition)
6	Russian Journal of Nonlinear Dynamics
5	Journal of Computational Physics
5	Journal of Mathematical Biology
5	Physica A
5	Reports on Mathematical Physics
...and 326 more Serials

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Cited in 63 Fields

2,963	Dynamical systems and ergodic theory (37-XX)
404	Differential geometry (53-XX)
358	Measure and integration (28-XX)
201	Ordinary differential equations (34-XX)
191	Manifolds and cell complexes (57-XX)
182	Global analysis, analysis on manifolds (58-XX)
159	General topology (54-XX)
151	Mechanics of particles and systems (70-XX)
143	Topological groups, Lie groups (22-XX)
142	Probability theory and stochastic processes (60-XX)
134	Number theory (11-XX)
125	Several complex variables and analytic spaces (32-XX)
114	Partial differential equations (35-XX)
94	Statistical mechanics, structure of matter (82-XX)
86	Operator theory (47-XX)
85	Group theory and generalizations (20-XX)
70	Systems theory; control (93-XX)
67	Quantum theory (81-XX)
65	Functions of a complex variable (30-XX)
55	Computer science (68-XX)
52	Biology and other natural sciences (92-XX)
48	Fluid mechanics (76-XX)
45	Functional analysis (46-XX)
45	Numerical analysis (65-XX)
45	Information and communication theory, circuits (94-XX)
39	Algebraic geometry (14-XX)
35	Difference and functional equations (39-XX)
32	Combinatorics (05-XX)
28	Convex and discrete geometry (52-XX)
26	Linear and multilinear algebra; matrix theory (15-XX)
24	Real functions (26-XX)
24	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
23	Algebraic topology (55-XX)
21	Abstract harmonic analysis (43-XX)
21	Calculus of variations and optimal control; optimization (49-XX)
21	Geometry (51-XX)
18	Statistics (62-XX)
15	Mathematical logic and foundations (03-XX)
13	\(K\)-theory (19-XX)
12	General and overarching topics; collections (00-XX)
12	Geophysics (86-XX)
11	History and biography (01-XX)
11	Optics, electromagnetic theory (78-XX)
11	Operations research, mathematical programming (90-XX)
10	Harmonic analysis on Euclidean spaces (42-XX)
8	Associative rings and algebras (16-XX)
8	Potential theory (31-XX)
8	Mechanics of deformable solids (74-XX)
7	Classical thermodynamics, heat transfer (80-XX)
7	Relativity and gravitational theory (83-XX)
6	Order, lattices, ordered algebraic structures (06-XX)
5	Category theory; homological algebra (18-XX)
4	Special functions (33-XX)
3	Field theory and polynomials (12-XX)
3	Commutative algebra (13-XX)
3	Nonassociative rings and algebras (17-XX)
3	Integral transforms, operational calculus (44-XX)
3	Astronomy and astrophysics (85-XX)
2	General algebraic systems (08-XX)
2	Integral equations (45-XX)
1	Sequences, series, summability (40-XX)
1	Approximations and expansions (41-XX)
1	Mathematics education (97-XX)

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