Richard Montgomery - Author Profile

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Montgomery, Richard

Author ID:	montgomery.richard
Published as:	Montgomery, Richard; Montgomery, R.
Homepage:	https://people.ucsc.edu/~rmont/
External Links:	MGP

Documents Indexed:	95 Publications since 1984, including 4 Books and 13 Additional arXiv Preprints
Co-Authors:	71 Co-Authors with 49 Joint Publications
	2,168 Co-Co-Authors

all top 5

Co-Authors

44	single-authored
7	Moeckel, Richard
6	Ehlers, Kurt M.
6	Koiller, Jair
5	Marsden, Jerrold Eldon
5	Ratiu, Tudor Stefan
4	Bor, Gil
3	Ribeiro Castro, Alex Lúcio
3	Chenciner, Alain
3	Féjoz, Jacques
3	Knauf, Andreas
3	Zhitomirskii, Michail
2	Delgado, Joaquín F.
2	Gotay, Mark J.
2	Le Donne, Enrico
1	Almeida, Maria de Fátima L. B. P.
1	Ardentov, Andrei A.
1	Bates, Larry M.
1	Bloch, Anthony Michael
1	Bravo-Doddoli, Alejandro
1	Cendra, Hernán
1	Cheng, Jih-Hsin
1	Cherman, Alexandre
1	Chorin, Alexandre Joel
1	Coli, Earnest W.
1	de M. Rios, Pedro
1	Delgado Fernández, Joaquín
1	Dellnitz, Michael
1	Desbrun, Mathieu
1	Diaconis, Persi Warren
1	Duda, Fernando Pereira
1	Duignan, Nathan
1	Dullin, Holger R.
1	Ercolani, Nicholas M.
1	Forest, Mark Gregory
1	Fujiwara, Toshiaki
1	Gerver, Joseph L.
1	Ginzburg, Viktor L’vovich
1	Golubitsky, Martin A.
1	Holmes, Susan P.
1	Isenberg, James A.
1	Isenberg, Jim
1	Jackman, Connor
1	Kaplan, Samuel R.
1	Kazaryan, Maxim Eduardovich
1	Keyfitz, Barbara Lee
1	Krishnaprasad, P.s.
1	Lerman, Eugene M.
1	Levy, Mark
1	Lewis, Debra
1	Marugame, Taiji
1	Matveev, Vladimir S.
1	McLaughlin, David W.
1	Ortiz, Michael
1	Ottazzi, Alessandro
1	Pansu, Pierre
1	Raugel, Geneviève
1	Raupp, Marco Antonio
1	Sachkov, Yuriĭ Leonidovich
1	Sánchez-Morgado, Héctor
1	Scheurle, Jürgen
1	Shanbrom, Corey
1	Shapiro, Boris Zalmanovich
1	Shapiro, Michael Z.
1	Simó, Carles
1	Sjamaar, Reyer
1	Stolin, Alexander
1	Stuchi, Teresinha J.
1	Swaminathan, Vidya
1	Venturelli, Andrea
1	Vittone, Davide
1	Weinstein, Alan David
1	Yoshimura, Hiroaki
1	Yu, Guowei

all top 5

Serials

8	Nonlinearity
5	Communications in Mathematical Physics
5	Pacific Journal of Mathematics
5	Regular and Chaotic Dynamics
3	Archive for Rational Mechanics and Analysis
2	Memoirs of the American Mathematical Society
2	Ergodic Theory and Dynamical Systems
2	Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2	Bulletin of the American Mathematical Society. New Series
2	Notices of the American Mathematical Society
2	Journal of Dynamical and Control Systems
1	American Mathematical Monthly
1	Israel Journal of Mathematics
1	Letters in Mathematical Physics
1	The Mathematical Intelligencer
1	Advances in Mathematics
1	Duke Mathematical Journal
1	Inventiones Mathematicae
1	Journal of Differential Equations
1	SIAM Journal on Control and Optimization
1	Physica D
1	MCSS. Mathematics of Control, Signals, and Systems
1	L’Enseignement Mathématique. 2e Série
1	SIAM Review
1	Celestial Mechanics and Dynamical Astronomy
1	Journal of Nonlinear Science
1	Computational and Applied Mathematics
1	Annals of Mathematics. Second Series
1	Qualitative Theory of Dynamical Systems
1	Miscelánea Matemática
1	Discrete and Continuous Dynamical Systems. Series B
1	SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
1	Mathematical Surveys and Monographs
1	Journal of Fixed Point Theory and Applications

all top 5

Fields

52	Mechanics of particles and systems (70-XX)
35	Dynamical systems and ergodic theory (37-XX)
33	Differential geometry (53-XX)
20	Global analysis, analysis on manifolds (58-XX)
7	Quantum theory (81-XX)
6	Ordinary differential equations (34-XX)
6	Mechanics of deformable solids (74-XX)
6	Fluid mechanics (76-XX)
5	Algebraic geometry (14-XX)
4	Calculus of variations and optimal control; optimization (49-XX)
3	General and overarching topics; collections (00-XX)
3	Topological groups, Lie groups (22-XX)
3	Several complex variables and analytic spaces (32-XX)
3	Partial differential equations (35-XX)
3	Biology and other natural sciences (92-XX)
3	Systems theory; control (93-XX)
2	History and biography (01-XX)
1	Nonassociative rings and algebras (17-XX)
1	Group theory and generalizations (20-XX)
1	Convex and discrete geometry (52-XX)
1	Manifolds and cell complexes (57-XX)
1	Probability theory and stochastic processes (60-XX)
1	Statistics (62-XX)
1	Statistical mechanics, structure of matter (82-XX)
1	Relativity and gravitational theory (83-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

74 Publications have been cited 1,859 times in 1,401 Documents	Cited by ▼	Year ▼
A tour of subriemannian geometries, their geodesics and applications. Zbl 1044.53022 Montgomery, Richard	537	2002
A remarkable periodic solution of the three-body problem in the case of equal masses. Zbl 0987.70009 Chenciner, Alain; Montgomery, Richard	191	2000
Reduction, symmetry, and phases in mechanics. Zbl 0713.58052 Marsden, J. E.; Montgomery, R.; Ratiu, T.	97	1990
Abnormal minimizers. Zbl 0816.49019 Montgomery, Richard	72	1994
The Hamiltonian structure for dynamic free boundary problems. Zbl 0638.58044 Lewis, Debra; Marsden, J.; Montgomery, R.; Ratiu, T.	58	1986
Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization. Zbl 1095.70007 Ehlers, Kurt; Koiller, Jair; Montgomery, Richard; Rios, Pedro M.	51	2005
Hearing the zero locus of a magnetic field. Zbl 0827.58076 Montgomery, Richard	47	1995
Isoholonomic problems and some applications. Zbl 0703.53024 Montgomery, R.	45	1990
The \(N\)-body problem, the braid group, and action-minimizing periodic solutions. Zbl 1076.70503 Montgomery, Richard	44	1998
Canonical formulations of a classical particle in a Yang-Mills field and Wong’s equations. Zbl 0562.53062 Montgomery, Richard	43	1984
Simple choreographic motions of \(N\) bodies: a preliminary study. Zbl 1146.70333 Chenciner, Alain; Gerver, Joseph; Montgomery, Richard; Simó, Carles	36	2002
Geometric approach to Goursat flags. Zbl 1013.58004 Montgomery, Richard; Zhitomirskii, Michail	33	2001
Gauged Lie-Poisson structures. Zbl 0546.58026 Montgomery, Richard; Marsden, Jerrold; Ratiu, Tudor	31	1984
A survey of singular curves in sub-Riemannian geometry. Zbl 0941.53021 Montgomery, R.	29	1995
The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case. Zbl 0689.58043 Montgomery, R.	28	1988
\(G_2\) and the rolling distribution. Zbl 1251.70008 Bor, Gil; Montgomery, Richard	26	2009
Examples of singular reduction. Zbl 0812.58034 Lerman, Eugene; Montgomery, Richard; Sjamaar, Reyer	24	1993
Sard property for the endpoint map on some Carnot groups. Zbl 1352.53025 Le Donne, Enrico; Montgomery, Richard; Ottazzi, Alessandro; Pansu, Pierre; Vittone, Davide	23	2016
Dynamical bias in the coin toss. Zbl 1513.62009 Diaconis, Persi; Holmes, Susan; Montgomery, Richard	22	2007
The three-body problem and the shape sphere. Zbl 1370.70034 Montgomery, Richard	20	2015
Rotating eights. I: The three \(\Gamma_i\) families. Zbl 1101.34025 Chenciner, Alain; Féjoz, Jacques; Montgomery, Richard	20	2005
Problems and progress in microswimming. Zbl 0867.76099 Koiller, J.; Ehlers, K.; Montgomery, R.	20	1996
Gauge theory of the falling cat. Zbl 0787.70020 Montgomery, Richard	18	1993
Singular extremals on Lie groups. Zbl 0925.93132 Montgomery, Richard	17	1994
Infinitely many syzygies. Zbl 1024.70005 Montgomery, Richard	17	2002
Engel deformations and contact structures. Zbl 0961.53043 Montgomery, Richard	16	1999
Points and curves in the monster tower. Zbl 1187.58006 Montgomery, Richard; Zhitomirskii, Michail	15	2010
Hamiltonian structure for the modulation equations of a sine-Gordon wavetrain. Zbl 0668.35064 Ercolani, N.; Forest, M. G.; McLaughlin, D. W.; Montgomery, R.	15	1987
From brake to syzygy. Zbl 1286.70014 Moeckel, Richard; Montgomery, Richard; Venturelli, Andrea	14	2012
Fitting hyperbolic pants to a three-body problem. Zbl 1069.70006 Montgomery, Richard	13	2005
Realizing all reduced syzygy sequences in the planar three-body problem. Zbl 1338.70018 Moeckel, Richard; Montgomery, Richard	12	2015
A nonintegrable sub-Riemannian geodesic flow on a Carnot group. Zbl 0941.53046 Montgomery, R.; Shapiro, M.; Stolin, A.	12	1997
The zero angular momentum, three-body problem: all but one solution has syzygies. Zbl 1128.70005 Montgomery, Richard	12	2007
Chains in CR geometry as geodesics of a Kropina metric. Zbl 1420.32025 Cheng, Jih-Hsin; Marugame, Taiji; Matveev, Vladimir S.; Montgomery, Richard	11	2019
Geometric quantization and no-go theorems. Zbl 0995.53056 Ginzburg, Viktor L.; Montgomery, Richard	11	2000
Generic distributions and Lie algebras of vector fields. Zbl 0782.58008 Montgomery, Richard	11	1993
Closed geodesics on the space of stable two-monopoles. Zbl 0820.53058 Bates, Larry; Montgomery, Richard	10	1988
Chazy-type asymptotics and hyperbolic scattering for the \(n\)-body problem. Zbl 1464.70007 Duignan, Nathan; Moeckel, Richard; Montgomery, Richard; Yu, Guowei	9	2020
Keplerian dynamics on the Heisenberg group and elsewhere. Zbl 1342.70041 Montgomery, Richard; Shanbrom, Corey	8	2015
Syzygies in the two center problem. Zbl 1358.37029 Dullin, Holger R.; Montgomery, Richard	8	2016
\(SO(3)\) invariant Yang-Mills fields which are not self-dual. Zbl 0776.53018 Bor, Gil; Montgomery, Richard	8	1990
Action spectrum and collisions in the planar three-body problem. Zbl 1151.70315 Montgomery, Richard	8	2002
Lagrangian relations and linear point billiards. Zbl 1375.37114 Féjoz, Jacques; Knauf, Andreas; Montgomery, Richard	8	2017
No hyperbolic pants for the 4-body problem with strong potential. Zbl 1362.37159 Jackman, Connor; Montgomery, Richard	7	2016
Optimal control of deformable bodies and its relation to gauge theory. Zbl 0758.53059 Montgomery, R.	7	1991
Spatial curve singularities and the monster/semple tower. Zbl 1266.58023 Castro, A. L.; Montgomery, R.	7	2012
Symmetric regularization, reduction and blow-up of the planar three-body problem. Zbl 1275.37037 Moeckel, Richard; Montgomery, Richard	7	2013
Survey of singular geodesics. Zbl 0868.53020 Montgomery, Richard	7	1996
Heisenberg and isoholonomic inequalities. Zbl 0744.58028 Montgomery, R.	7	1991
Free time minimizers for the three-body problem. Zbl 1390.70022 Moeckel, Richard; Montgomery, Richard; Sánchez Morgado, Héctor	7	2018
The geometric phase of the three-body problem. Zbl 0928.70022 Montgomery, Richard	6	1996
Cartan-Hannay-Berry phases and symmetry. Zbl 0694.70008 Marsden, J.; Montgomery, R.; Ratiu, T.	6	1989
Low Reynolds number swimming in two dimensions. Zbl 0999.76147 Cherman, Alexandre; Delgado, Joaquín; Duda, Fernando; Ehlers, Kurt; Koiller, Jair; Montgomery, Richard	5	2000
A new solution to the three-body problem. Zbl 1047.70036 Montgomery, Richard	5	2001
Bicycle paths, elasticae and sub-Riemannian geometry. Zbl 1468.53029 Ardentov, Andrei; Bor, Gil; Le Donne, Enrico; Montgomery, Richard; Sachkov, Yuri	4	2021
The chains of left-invariant Cauchy-Riemann structures on \(SU(2)\). Zbl 1152.32016 Castro, Alex L.; Montgomery, Richard	4	2008
Characteristic classes for the degenerations of two-plane fields in four dimensions. Zbl 0895.58004 Kazarian, Maxim; Montgomery, Richard; Shapiro, Boris	4	1997
Geodesics in jet space. Zbl 1532.53056 Bravo-Doddoli, Alejandro; Montgomery, Richard	3	2022
Spectral methods for Stokes flows. Zbl 0916.76053 Koiller, J.; Raupp, M. A.; Delgado, J.; Ehlers, K. M.; Montgomery, R.	3	1998
Convexity of the figure eight solution to the three-body problem. Zbl 1082.70005 Fujiwara, Toshiaki; Montgomery, Richard	3	2005
Nonholonomic control and gauge theory. Zbl 0788.70021 Montgomery, Richard	3	1992
Classical \(n\)-body scattering with long-range potentials. Zbl 1493.70057 Fejoz, Jacques; Knauf, Andreas; Montgomery, Richard	3	2021
Who’s afraid of the Hill boundary? Zbl 1370.37120 Montgomery, Richard	2	2014
Minimizers for the Kepler problem. Zbl 1462.70006 Montgomery, Richard	2	2020
Oscillating about coplanarity in the 4 body problem. Zbl 1435.70031 Montgomery, Richard	2	2019
MICZ-Kepler: dynamics on the cone over \(\mathrm{SO}(n)\). Zbl 1286.70012 Montgomery, Richard	1	2013
Momentum maps and geometic phases. Zbl 1050.70001 Koiller, Jair; Coli, Earnest W.; Montgomery, Richard; Delgado-Fernández, Joaquín; Ehlers, Kurt; Stüchi, Teresinha J.; Almeida, Maria de Fátima L. B. P.	1	2002
Making the moon reverse its orbit, or, stuttering in the planar three-body problem. Zbl 1147.70006 Kaplan, Samuel R.; Levy, Mark; Montgomery, Richard	1	2008
Resolving singularities with Cartan’s prolongation. Zbl 1153.14004 Montgomery, Richard; Swaminathan, Vidya; Zhitomirskii, Mikhail	1	2008
Book review of: A. Agrachev et al., A comprehensive introduction to sub-Riemannian geometry. From the Hamiltonian viewpoint. Zbl 1492.00024 Montgomery, Richard	1	2020
Introduction to a paper of M. Z. Shapiro: Homotopy theory in control. Zbl 0864.93037 Montgomery, Richard	1	1996
Compactification of the energy surfaces for \(n\) bodies. Zbl 07765044 Knauf, Andreas; Montgomery, Richard	1	2023
The hyperbolic plane, three-body problems, and Mnëv’s universality theorem. Zbl 1387.70014 Montgomery, Richard	1	2017
Dropping bodies. Zbl 1523.70016 Montgomery, Richard	1	2023
Compactification of the energy surfaces for \(n\) bodies. Zbl 07765044 Knauf, Andreas; Montgomery, Richard	1	2023
Dropping bodies. Zbl 1523.70016 Montgomery, Richard	1	2023
Geodesics in jet space. Zbl 1532.53056 Bravo-Doddoli, Alejandro; Montgomery, Richard	3	2022
Bicycle paths, elasticae and sub-Riemannian geometry. Zbl 1468.53029 Ardentov, Andrei; Bor, Gil; Le Donne, Enrico; Montgomery, Richard; Sachkov, Yuri	4	2021
Classical \(n\)-body scattering with long-range potentials. Zbl 1493.70057 Fejoz, Jacques; Knauf, Andreas; Montgomery, Richard	3	2021
Chazy-type asymptotics and hyperbolic scattering for the \(n\)-body problem. Zbl 1464.70007 Duignan, Nathan; Moeckel, Richard; Montgomery, Richard; Yu, Guowei	9	2020
Minimizers for the Kepler problem. Zbl 1462.70006 Montgomery, Richard	2	2020
Book review of: A. Agrachev et al., A comprehensive introduction to sub-Riemannian geometry. From the Hamiltonian viewpoint. Zbl 1492.00024 Montgomery, Richard	1	2020
Chains in CR geometry as geodesics of a Kropina metric. Zbl 1420.32025 Cheng, Jih-Hsin; Marugame, Taiji; Matveev, Vladimir S.; Montgomery, Richard	11	2019
Oscillating about coplanarity in the 4 body problem. Zbl 1435.70031 Montgomery, Richard	2	2019
Free time minimizers for the three-body problem. Zbl 1390.70022 Moeckel, Richard; Montgomery, Richard; Sánchez Morgado, Héctor	7	2018
Lagrangian relations and linear point billiards. Zbl 1375.37114 Féjoz, Jacques; Knauf, Andreas; Montgomery, Richard	8	2017
The hyperbolic plane, three-body problems, and Mnëv’s universality theorem. Zbl 1387.70014 Montgomery, Richard	1	2017
Sard property for the endpoint map on some Carnot groups. Zbl 1352.53025 Le Donne, Enrico; Montgomery, Richard; Ottazzi, Alessandro; Pansu, Pierre; Vittone, Davide	23	2016
Syzygies in the two center problem. Zbl 1358.37029 Dullin, Holger R.; Montgomery, Richard	8	2016
No hyperbolic pants for the 4-body problem with strong potential. Zbl 1362.37159 Jackman, Connor; Montgomery, Richard	7	2016
The three-body problem and the shape sphere. Zbl 1370.70034 Montgomery, Richard	20	2015
Realizing all reduced syzygy sequences in the planar three-body problem. Zbl 1338.70018 Moeckel, Richard; Montgomery, Richard	12	2015
Keplerian dynamics on the Heisenberg group and elsewhere. Zbl 1342.70041 Montgomery, Richard; Shanbrom, Corey	8	2015
Who’s afraid of the Hill boundary? Zbl 1370.37120 Montgomery, Richard	2	2014
Symmetric regularization, reduction and blow-up of the planar three-body problem. Zbl 1275.37037 Moeckel, Richard; Montgomery, Richard	7	2013
MICZ-Kepler: dynamics on the cone over \(\mathrm{SO}(n)\). Zbl 1286.70012 Montgomery, Richard	1	2013
From brake to syzygy. Zbl 1286.70014 Moeckel, Richard; Montgomery, Richard; Venturelli, Andrea	14	2012
Spatial curve singularities and the monster/semple tower. Zbl 1266.58023 Castro, A. L.; Montgomery, R.	7	2012
Points and curves in the monster tower. Zbl 1187.58006 Montgomery, Richard; Zhitomirskii, Michail	15	2010
\(G_2\) and the rolling distribution. Zbl 1251.70008 Bor, Gil; Montgomery, Richard	26	2009
The chains of left-invariant Cauchy-Riemann structures on \(SU(2)\). Zbl 1152.32016 Castro, Alex L.; Montgomery, Richard	4	2008
Making the moon reverse its orbit, or, stuttering in the planar three-body problem. Zbl 1147.70006 Kaplan, Samuel R.; Levy, Mark; Montgomery, Richard	1	2008
Resolving singularities with Cartan’s prolongation. Zbl 1153.14004 Montgomery, Richard; Swaminathan, Vidya; Zhitomirskii, Mikhail	1	2008
Dynamical bias in the coin toss. Zbl 1513.62009 Diaconis, Persi; Holmes, Susan; Montgomery, Richard	22	2007
The zero angular momentum, three-body problem: all but one solution has syzygies. Zbl 1128.70005 Montgomery, Richard	12	2007
Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization. Zbl 1095.70007 Ehlers, Kurt; Koiller, Jair; Montgomery, Richard; Rios, Pedro M.	51	2005
Rotating eights. I: The three \(\Gamma_i\) families. Zbl 1101.34025 Chenciner, Alain; Féjoz, Jacques; Montgomery, Richard	20	2005
Fitting hyperbolic pants to a three-body problem. Zbl 1069.70006 Montgomery, Richard	13	2005
Convexity of the figure eight solution to the three-body problem. Zbl 1082.70005 Fujiwara, Toshiaki; Montgomery, Richard	3	2005
A tour of subriemannian geometries, their geodesics and applications. Zbl 1044.53022 Montgomery, Richard	537	2002
Simple choreographic motions of \(N\) bodies: a preliminary study. Zbl 1146.70333 Chenciner, Alain; Gerver, Joseph; Montgomery, Richard; Simó, Carles	36	2002
Infinitely many syzygies. Zbl 1024.70005 Montgomery, Richard	17	2002
Action spectrum and collisions in the planar three-body problem. Zbl 1151.70315 Montgomery, Richard	8	2002
Momentum maps and geometic phases. Zbl 1050.70001 Koiller, Jair; Coli, Earnest W.; Montgomery, Richard; Delgado-Fernández, Joaquín; Ehlers, Kurt; Stüchi, Teresinha J.; Almeida, Maria de Fátima L. B. P.	1	2002
Geometric approach to Goursat flags. Zbl 1013.58004 Montgomery, Richard; Zhitomirskii, Michail	33	2001
A new solution to the three-body problem. Zbl 1047.70036 Montgomery, Richard	5	2001
A remarkable periodic solution of the three-body problem in the case of equal masses. Zbl 0987.70009 Chenciner, Alain; Montgomery, Richard	191	2000
Geometric quantization and no-go theorems. Zbl 0995.53056 Ginzburg, Viktor L.; Montgomery, Richard	11	2000
Low Reynolds number swimming in two dimensions. Zbl 0999.76147 Cherman, Alexandre; Delgado, Joaquín; Duda, Fernando; Ehlers, Kurt; Koiller, Jair; Montgomery, Richard	5	2000
Engel deformations and contact structures. Zbl 0961.53043 Montgomery, Richard	16	1999
The \(N\)-body problem, the braid group, and action-minimizing periodic solutions. Zbl 1076.70503 Montgomery, Richard	44	1998
Spectral methods for Stokes flows. Zbl 0916.76053 Koiller, J.; Raupp, M. A.; Delgado, J.; Ehlers, K. M.; Montgomery, R.	3	1998
A nonintegrable sub-Riemannian geodesic flow on a Carnot group. Zbl 0941.53046 Montgomery, R.; Shapiro, M.; Stolin, A.	12	1997
Characteristic classes for the degenerations of two-plane fields in four dimensions. Zbl 0895.58004 Kazarian, Maxim; Montgomery, Richard; Shapiro, Boris	4	1997
Problems and progress in microswimming. Zbl 0867.76099 Koiller, J.; Ehlers, K.; Montgomery, R.	20	1996
Survey of singular geodesics. Zbl 0868.53020 Montgomery, Richard	7	1996
The geometric phase of the three-body problem. Zbl 0928.70022 Montgomery, Richard	6	1996
Introduction to a paper of M. Z. Shapiro: Homotopy theory in control. Zbl 0864.93037 Montgomery, Richard	1	1996
Hearing the zero locus of a magnetic field. Zbl 0827.58076 Montgomery, Richard	47	1995
A survey of singular curves in sub-Riemannian geometry. Zbl 0941.53021 Montgomery, R.	29	1995
Abnormal minimizers. Zbl 0816.49019 Montgomery, Richard	72	1994
Singular extremals on Lie groups. Zbl 0925.93132 Montgomery, Richard	17	1994
Examples of singular reduction. Zbl 0812.58034 Lerman, Eugene; Montgomery, Richard; Sjamaar, Reyer	24	1993
Gauge theory of the falling cat. Zbl 0787.70020 Montgomery, Richard	18	1993
Generic distributions and Lie algebras of vector fields. Zbl 0782.58008 Montgomery, Richard	11	1993
Nonholonomic control and gauge theory. Zbl 0788.70021 Montgomery, Richard	3	1992
Optimal control of deformable bodies and its relation to gauge theory. Zbl 0758.53059 Montgomery, R.	7	1991
Heisenberg and isoholonomic inequalities. Zbl 0744.58028 Montgomery, R.	7	1991
Reduction, symmetry, and phases in mechanics. Zbl 0713.58052 Marsden, J. E.; Montgomery, R.; Ratiu, T.	97	1990
Isoholonomic problems and some applications. Zbl 0703.53024 Montgomery, R.	45	1990
\(SO(3)\) invariant Yang-Mills fields which are not self-dual. Zbl 0776.53018 Bor, Gil; Montgomery, Richard	8	1990
Cartan-Hannay-Berry phases and symmetry. Zbl 0694.70008 Marsden, J.; Montgomery, R.; Ratiu, T.	6	1989
The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case. Zbl 0689.58043 Montgomery, R.	28	1988
Closed geodesics on the space of stable two-monopoles. Zbl 0820.53058 Bates, Larry; Montgomery, Richard	10	1988
Hamiltonian structure for the modulation equations of a sine-Gordon wavetrain. Zbl 0668.35064 Ercolani, N.; Forest, M. G.; McLaughlin, D. W.; Montgomery, R.	15	1987
The Hamiltonian structure for dynamic free boundary problems. Zbl 0638.58044 Lewis, Debra; Marsden, J.; Montgomery, R.; Ratiu, T.	58	1986
Canonical formulations of a classical particle in a Yang-Mills field and Wong’s equations. Zbl 0562.53062 Montgomery, Richard	43	1984
Gauged Lie-Poisson structures. Zbl 0546.58026 Montgomery, Richard; Marsden, Jerrold; Ratiu, Tudor	31	1984

all cited Publications top 5 cited Publications

all top 5

Cited by 1,409 Authors

30	Marsden, Jerrold Eldon
29	Sachkov, Yuriĭ Leonidovich
23	Montgomery, Richard
20	Yan, Duokui
18	Agrachev, Andreĭ Aleksandrovich
17	Le Donne, Enrico
16	Helffer, Bernard
16	Markina, Irina
15	Barilari, Davide
15	Boscain, Ugo
15	Grong, Erlend
15	Rizzi, Luca
14	Citti, Giovanna
13	Ouyang, Tiancheng
13	Terracini, Susanna
12	Mamaev, Ivan Sergeevich
12	Ratiu, Tudor Stefan
11	García-Naranjo, Luis C.
11	Pinamonti, Andrea
11	Vorob’ev, Yu. M.
10	Avendaño-Camacho, Misael
10	Borisov, Alekseĭ Vladimirovich
10	de León Rodríguez, Manuel
10	Koiller, Jair
10	Trélat, Emmanuel
10	Vittone, Davide
10	Zhang, Shiqing
9	Monti, Roberto
9	Sachkova, Elena F.
9	Shibayama, Mitsuru
9	Tyson, Jeremy T.
9	Yu, Guowei
8	Barutello, Vivina L.
8	Bloch, Anthony Michael
8	García-Azpeitia, Carlos
8	Holm, Darryl Dallas
8	Hu, Xijun
8	Kilin, Aleksandr Aleksandrovich
8	Mashtakov, Alexey P.
8	Ottazzi, Alessandro
8	Pelletier, Fernand
8	Shanbrom, Corey
8	Shashikanth, Banavara N.
8	Speight, Gareth
7	Bauer, Wolfram
7	Bonnard, Bernard
7	Capogna, Luca
7	Chang, Der-Chen E.
7	Franchi, Bruno
7	Garofalo, Nicola
7	Gay-Balmaz, François
7	Gordina, Maria
7	Jovanović, Božidar Žarko
7	Kordyukov, Yuri A.
7	Marrero Gonzalez, Juan Carlos
7	Martini, Alessio
7	Prandi, Dario
7	Raymond, Nicolas
7	Rifford, Ludovic
7	Ritoré, Manuel
7	Solov’ev, Vladimir O.
6	Balseiro, Paula
6	Boarotto, Francesco
6	Bor, Gil
6	Chitour, Yacine
6	del Pino, Álvaro
6	Dragoni, Federica
6	Duits, Remco
6	Fernandez, Oscar E.
6	Godoy Molina, Mauricio
6	Juillet, Nicolas
6	Lewis, Debra
6	Mestdag, Tom
6	Miranda, Eva
6	Simmons, Skyler Clayson
6	Tronci, Cesare
5	Baldi, Annalisa
5	Biggs, Rory
5	Bravo-Doddoli, Alejandro
5	Cannarsa, Piermarco
5	Ribeiro Castro, Alex Lúcio
5	Chen, Hua
5	Diacu, Florin Nicolae
5	Dullin, Holger R.
5	Ercolani, Nicholas M.
5	Féjoz, Jacques
5	Gauthier, Jean-Paul A.
5	Grochowski, Marek
5	Gronchi, Giovanni-Federico
5	Jackman, Connor
5	Karmanova, Mariya Borisovna
5	Knauf, Andreas
5	Krishnaprasad, P.s.
5	Lee, Paul W. Y.
5	Li, Sean
5	Martín de Diego, David
5	Matveev, Vladimir S.
5	McLaughlin, David W.
5	Montefalcone, Francescopaolo
5	Ohsawa, Tomoki
...and 1,309 more Authors

all top 5

Cited in 311 Serials

64	Journal of Geometry and Physics
49	Journal of Dynamical and Control Systems
46	Regular and Chaotic Dynamics
40	Journal of Mathematical Physics
39	Archive for Rational Mechanics and Analysis
33	Celestial Mechanics and Dynamical Astronomy
32	Communications in Mathematical Physics
31	Nonlinearity
28	Calculus of Variations and Partial Differential Equations
27	Physica D
26	Journal of Differential Equations
26	Journal of Nonlinear Science
25	Transactions of the American Mathematical Society
25	Differential Geometry and its Applications
25	European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
23	The Journal of Geometric Analysis
21	Journal of Functional Analysis
18	Advances in Mathematics
18	Journal of Geometric Mechanics
17	Reports on Mathematical Physics
16	Journal of Mathematical Sciences (New York)
14	Journal of Physics A: Mathematical and Theoretical
13	Journal of Mathematical Analysis and Applications
13	Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
13	Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
13	Discrete and Continuous Dynamical Systems
13	SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
12	Letters in Mathematical Physics
12	Qualitative Theory of Dynamical Systems
11	Journal de Mathématiques Pures et Appliquées. Neuvième Série
11	Analysis and Geometry in Metric Spaces
10	Annales de l’Institut Fourier
9	Annali di Matematica Pura ed Applicata. Serie Quarta
9	Mathematische Annalen
9	Potential Analysis
9	Analysis and Mathematical Physics
8	Theoretical and Mathematical Physics
8	Russian Journal of Mathematical Physics
8	Doklady Mathematics
8	Comptes Rendus. Mathématique. Académie des Sciences, Paris
8	International Journal of Geometric Methods in Modern Physics
7	Inventiones Mathematicae
7	Mathematische Zeitschrift
7	Acta Applicandae Mathematicae
7	Sbornik: Mathematics
7	Proceedings of the Steklov Institute of Mathematics
6	Physics Letters. A
6	Proceedings of the American Mathematical Society
6	Annals of Global Analysis and Geometry
6	Revista Matemática Iberoamericana
6	Journal of Mathematical Imaging and Vision
6	Bulletin des Sciences Mathématiques
6	Lobachevskii Journal of Mathematics
6	Differential Equations
5	Memoirs of the American Mathematical Society
5	Ergodic Theory and Dynamical Systems
5	Geometric and Functional Analysis. GAFA
5	Communications in Partial Differential Equations
5	Journal of Dynamics and Differential Equations
5	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
5	Physics of Fluids
5	Communications in Nonlinear Science and Numerical Simulation
5	Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
4	International Journal of Modern Physics A
4	Israel Journal of Mathematics
4	Mathematical Notes
4	Automatica
4	Duke Mathematical Journal
4	Pacific Journal of Mathematics
4	Chaos
4	Advanced Nonlinear Studies
4	Foundations of Physics
4	Frontiers of Mathematics in China
4	Journal of Spectral Theory
4	Russian Journal of Nonlinear Dynamics
3	International Journal of Theoretical Physics
3	Journal d’Analyse Mathématique
3	The Mathematical Intelligencer
3	The Annals of Probability
3	Geometriae Dedicata
3	Journal of Pure and Applied Algebra
3	Results in Mathematics
3	SIAM Journal on Control and Optimization
3	Siberian Mathematical Journal
3	Studies in Applied Mathematics
3	Systems & Control Letters
3	Chinese Annals of Mathematics. Series B
3	MCSS. Mathematics of Control, Signals, and Systems
3	Annals of Physics
3	Turkish Journal of Mathematics
3	Journal of Lie Theory
3	Revista Matemática Complutense
3	Acta Mathematica Sinica. English Series
3	Journal of High Energy Physics
3	Journal of Nonlinear Mathematical Physics
3	Acta Mathematica Scientia. Series B. (English Edition)
3	Bulletin of the Brazilian Mathematical Society. New Series
3	SIAM Journal on Applied Dynamical Systems
3	Journal of the Institute of Mathematics of Jussieu
3	Theoretical and Applied Mechanics
...and 211 more Serials

all top 5

Cited in 58 Fields

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

Montgomery, Richard

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Cited by 1,409 Authors

Cited in 311 Serials

Cited in 58 Fields

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