The life and mathematics of Jaroslav Smítal. (English) Zbl 1511.01050
Summary: Jaroslav Smítal was a distinguished Czech and Slovak mathematician. The first part of the article is devoted to important moments of his life. In the second part we briefly discuss some of his scientific results.
MSC:
| 01A70 | Biographies, obituaries, personalia, bibliographies |
| 37-03 | History of dynamical systems and ergodic theory |
Biographic References:
Smítal, JaroslavReferences:
| [1] | J. Smítal, On the structure of the space L (p) , Acta Fac. Natur. Univ. Comenian. Math. 10 (1966), 43-48. |
| [2] | T. Neubrunn, J. Smítal and T. Šalát, On certain properties charac-terizing locally separable metric spaces, Časopis Pěst. Mat. 92 (1967), 157-161. · Zbl 0171.43701 |
| [3] | J. Smítal and T. Šalát, Bemerkung zur Approximation der stetigen Funktionen durch Polynome, Acta Fac. Rerum Natur. Univ. Comenian. Math. 16 (1967), 43-47. · Zbl 0172.07803 |
| [4] | J. Smítal, On the functional equation f (x + y) = f (x) + f (y), Rev. Roumaine Math. Pures Appl. 13 (1968), 555-561. · Zbl 0165.50002 |
| [5] | T. Neubrunn, J. Smítal and T. Šalát, On the structure of the space M (0, 1), Rev. Roumaine Math. Pures Appl. 13 (1968), 377-386. · Zbl 0174.43903 |
| [6] | P. Kostyrko, J. Smítal and T. Šalát, Remarks on the theory of real functions, Acta Fac. Rerum Natur. Univ. Comenian. Math. 20 (1969), 81-89. · Zbl 0208.32403 |
| [7] | J. Smítal, On approximation of Baire functions by Darboux functions, Czechoslovak Math. J. 21(96) (1971), 418-423. · Zbl 0219.26005 |
| [8] | J. Smítal, On a problem concerning uniform limits of Darboux func-tions, Colloq. Math. 23 (1971), 115-116. · Zbl 0219.26006 |
| [9] | J. Smítal, Remarks on ratio sets of sets of natural numbers, Acta Fac. Rerum Natur. Univ. Comenian. Math. 25 (1971), 93-99. · Zbl 0228.10036 |
| [10] | J. Smítal, Some characterizations of the Darboux continuity of real functions, Mat. Časopis Sloven. Akad. Vied 22 (1972), 59-70. · Zbl 0228.26007 |
| [11] | J. Smítal, A note on the class M ′ 2 , Acta Fac. Rerum Natur. Univ. |
| [12] | Comenian. Math. 27 (1972), 97-99. · Zbl 0248.26004 |
| [13] | J. Smítal, On boundedness and discontinuity of additive functions, Fund. Math. 76 (1972), 245-253. · Zbl 0246.26008 |
| [14] | J. Smítal, Characteristic types of convergence for certain classes of Darboux-Baire one functions, Mat. Časopis Sloven. Akad. Vied 23 (1973), 115-118. · Zbl 0271.26004 |
| [15] | J. Smítal, A necessary and sufficient condition for continuity of additive functions, Czechoslovak Math. J. 26(101) (1976), 171-173. · Zbl 0332.26005 |
| [16] | M. Kuczma and J. Smítal, On measures connected with the Cauchy equation, Aequationes Math. 14 (1976), 421-428. · Zbl 0326.39007 |
| [17] | J. Smítal, On the sum of continuous and Darboux functions, Proc. Amer. Math. Soc. 60 (1976), 183-184. · Zbl 0339.26006 |
| [18] | J. Smítal, On convex functions bounded below, Aequationes Math. 14 (1976), 345-350. · Zbl 0324.26006 |
| [19] | P. Kostyrko and J. Smítal, The fiftieth birthday of Professor Tibor Šalát, Pokroky Mat. Fyz. Astronom. 21 (1976), 226-227. · Zbl 0329.01021 |
| [20] | P. Kostyrko, T. Neubrunn, J. Smítal and T. Šalát, On locally sym-metric and symmetrically continuous functions, Real Anal. Exchange 6 (1980/81), 67-76. · Zbl 0459.26001 |
| [21] | P. Kostyrko, T. Neubrunn, T. Šalát and J. Smítal, Remarks on the the-ory of real functions, Acta Fac. Rerum Natur. Univ. Comenian. Math. 36 (1980), 7-23. |
| [22] | J. Smítal and T. Šalát, Remarks on two generalizations of the notion of continuity, Acta Fac. Rerum Natur. Univ. Comenian. Math. 36 (1980), 115-119. · Zbl 0531.26001 |
| [23] | J. Smítal and E. Stanová, On almost continuous functions, Acta Math. Univ. Comenian. 37 (1980), 147-155. · Zbl 0554.26003 |
| [24] | J. Smítal and Ľ. Snoha, Generalization of a theorem of S. Piccard, Acta Math. Univ. Comenian. 37 (1980), 173-181. · Zbl 0526.26005 |
| [25] | J. Smítal, Iterates of piecewise monotonic continuous functions, Math. Slovaca 32 (1982), 143-146. · Zbl 0498.26003 |
| [26] | Ľ. Snoha |
| [27] | J. Smítal and K. Smítalová, Structural stability of nonchaotic difference equations, J. Math. Anal. Appl. 90 (1982), 1-11. · Zbl 0505.39004 |
| [28] | J. Smítal, A chaotic function with some extremal properties, Proc. Amer. Math. Soc. 87 (1983), 54-56. · Zbl 0555.26003 |
| [29] | J. Smítal and E. Kubáčková, On weakly closed functions, Acta Math. Univ. Comenian. 42/43 (1983), 115-120. · Zbl 0597.54014 |
| [30] | J. Smítal and K. Neubrunnová, Stability of typical continuous functions with respect to some properties of their iterates, Proc. Amer. Math. Soc. 90 (1984), 321-324. · Zbl 0529.54038 |
| [31] | J. Smítal and K. Smítalová, Erratum: “Structural stability of non-chaotic difference equations” [J. Math. Anal. Appl. 90 (1982), no. 1, 1-11], J. Math. Anal. Appl. 101 (1984), 324. |
| [32] | J. Smítal, A chaotic function with a scrambled set of positive Lebesgue measure, Proc. Amer. Math. Soc. 92 (1984), 50-54. · Zbl 0592.26006 |
| [33] | J. Smítal, On a problem of Aczél and Erdős concerning Hamel bases, Aequationes Math. 28 (1985), 135-137. · Zbl 0558.12011 |
| [34] | J. Smítal, Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297 (1986), 269-282. · Zbl 0639.54029 |
| [35] | K. Janková and J. Smítal, A characterization of chaos, Bull. Austral. Math. Soc. 34 (1986), 283-292. · Zbl 0577.54041 |
| [36] | M. Misiurewicz and J. Smítal, Smooth chaotic maps with zero topolog-ical entropy, Ergodic Theory Dynam. Systems 8 (1988), 421-424. · Zbl 0689.58028 |
| [37] | D. Preiss and J. Smítal, A characterization of nonchaotic continuous maps of the interval stable under small perturbations, Trans. Amer. Math. Soc. 313 (1989), 687-696. · Zbl 0698.58033 |
| [38] | J. Smítal, On Darboux solutions of the Euler’s equation, Aequationes Math. 37 (1989), 279-281. · Zbl 0674.39006 |
| [39] | K. Janková and J. Smítal, A theorem of Šarkovskiȋ characterizing con-tinuous maps of zero topological entropy, Math. Slovaca 39 (1989), 261-265. · Zbl 0686.26002 |
| [40] | V. V. Fedorenko, A. N. Sharkovskiȋ and J. Smítal, Characterization of some classes of mappings of an interval with zero topological entropy, Akad. Nauk Ukrain. SSR Inst. Mat. Preprint (1989), no. 58, 18 pages. |
| [41] | P. Kostyrko and J. Smítal, Professor Neubrunn (on the occasion of his 60th birthday), Časopis Pěst. Mat. 114 (1989), 214-218. · Zbl 0668.01026 |
| [42] | M. Kuchta and J. Smítal, Two-point scrambled set implies chaos, Eu-ropean Conference on Iteration Theory (Caldes de Malavella, 1987) (1989), 427-430. |
| [43] | V. V. Fedorenko, A. N. Šarkovskiȋ and J. Smítal, Characterizations of weakly chaotic maps of the interval, Proc. Amer. Math. Soc. 110 (1990), 141-148. · Zbl 0728.26008 |
| [44] | N. Franzová and J. Smítal, Positive sequence topological entropy char-acterizes chaotic maps, Proc. Amer. Math. Soc. 112 (1991), 1083-1086. · Zbl 0735.26005 |
| [45] | V. V. Fedorenko and J. Smítal, Maps of the interval Ljapunov stable on the set of nonwandering points, Acta Math. Univ. Comenian. (N.S.) 60 (1991), 11-14. · Zbl 0736.58027 |
| [46] | J. Smítal, In memory of Professor Neubrunn, Math. Bohem. 116 (1991), 445. · Zbl 0737.01018 |
| [47] | J. Smítal, Solution of a problem by Prof. Targoński concerning semicon-jugated maps, European Conference on Iteration Theory (Batschuns, 1989) (1991), 382-383. · Zbl 0986.37502 |
| [48] | A. M. Bruckner and J. Smítal, The structure of ω-limit sets for contin-uous maps of the interval, Math. Bohem. 117 (1992), 42-47. · Zbl 0762.26003 |
| [49] | A. M. Bruckner and J. Smítal, A characterization of ω-limit sets of maps of the interval with zero topological entropy, Ergodic Theory Dy-nam. Systems 13 (1993), 7-19. · Zbl 0788.58021 |
| [50] | E. M. Coven and J. Smítal, Entropy-minimality, Acta Math. Univ. Comenian. (N.S.) 62 (1993), 117-121. · Zbl 0826.54030 |
| [51] | F. Balibrea and J. Smítal, A chaotic continuous map generates all prob-ability distributions, J. Math. Anal. Appl. 180 (1993), 587-598. · Zbl 0794.60009 |
| [52] | B. Schweizer and J. Smítal, Measures of chaos and a spectral decompo-sition of dynamical systems on the interval, Trans. Amer. Math. Soc. 344 (1994), 737-754. · Zbl 0812.58062 |
| [53] | P. Kahlig and J. Smítal, On the solutions of a functional equation of Dhombres, Results Math. 27 (1995), 362-367. · Zbl 0860.39030 |
| [54] | Ľ. Snoha |
| [55] | G. L. Forti, L. Paganoni and J. Smítal, Strange triangular maps of the square, Bull. Austral. Math. Soc. 51 (1995), 395-415. · Zbl 0832.54033 |
| [56] | K. Janková and J. Smítal, Maps with random perturbations are gener-ically not chaotic, Proceedings of the Conference “Thirty Years after Sharkovskiȋ”s Theorem: New Perspectives” (Murcia, 1994), Internat. J. Bifur. Chaos Appl. Sci. Engrg. 5 (1995), 1375-1378. · Zbl 0886.58027 |
| [57] | F. Balibrea and J. Smítal, A characterization of the set Ω(f ) ω(f ) for continuous maps of the interval with zero topological entropy, Pro-ceedings of the Conference “Thirty Years after Sharkovskiȋ”s Theorem: New Perspectives” (Murcia, 1994), Internat. J. Bifur. Chaos Appl. Sci. Engrg. 5 (1995), 1433-1435. · Zbl 0886.58019 |
| [58] | F. Balibrea and J. Smítal, A characterization of the set Ω(f ) ω(f ) for continuous maps of the interval with zero topological entropy, Real Anal. Exchange 21 (1995/96), 622-628. · Zbl 0879.26017 |
| [59] | K. Janková and J. Smítal, Maps with random perturbations are gener-ically not chaotic, Thirty years after Sharkovskiȋ’s theorem: new per-spectives (Murcia, 1994), World Sci. Ser. Nonlinear Sci. Ser. B Spec. Theme Issues Proc. 8 (1995), 113-116. Reprint of [S53]. |
| [60] | F. Balibrea and J. Smítal, A characterization of the set Ω(f ) ω(f ) for continuous maps of the interval with zero topological entropy, Thirty years after Sharkovskiȋ’s theorem: new perspectives (Murcia, 1994), World Sci. Ser. Nonlinear Sci. Ser. B Spec. Theme Issues Proc. 8 (1995), 171-173. Reprint of [S54]. |
| [61] | A. Blokh, A. M. Bruckner, P. D. Humke and J. Smítal, The space of ω-limit sets of a continuous map of the interval, Trans. Amer. Math. Soc. 348 (1996), 1357-1372. · Zbl 0860.54036 |
| [62] | P. Kahlig and J. Smítal, On a parametric functional equation of Dhom-bres type, Aequationes Math. 56 (1998), 63-68. · Zbl 0915.39011 |
| [63] | G. L. Forti, L. Paganoni and J. Smítal, Dynamics of homeomorphisms on minimal sets generated by triangular mappings, Bull. Austral. Math. Soc. 59 (1999), 1-20. · Zbl 0976.54043 |
| [64] | L. Alsedà, M. Chas and J. Smítal, On the structure of the ω-limit sets for continuous maps of the interval, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 9 (1999), 1719-1729. · Zbl 1089.37514 |
| [65] | D. Pokluda and J. Smítal, A “universal” dynamical system generated by a continuous map of the interval, Proc. Amer. Math. Soc. 128 (2000), 3047-3056. · Zbl 0973.37025 |
| [66] | A. Sklar and J. Smítal, Distributional chaos on compact metric spaces via specification properties, J. Math. Anal. Appl. 241 (2000), 181-188. · Zbl 1060.37012 |
| [67] | V. Jiménez López and J. Smítal, Two counterexamples to a conjecture by Agronsky and Ceder, Acta Math. Hungar. 88 (2000), 193-204. · Zbl 0959.54011 |
| [68] | B. Schweizer, A. Sklar and J. Smítal, Distributional (and other) chaos and its measurement, Real Anal. Exchange 26 (2000/01), 495-524. · Zbl 1012.37022 |
| [69] | V. Jiménez López and J. Smítal, ω-limit sets for triangular mappings, Fund. Math. 167 (2001), 1-15. · Zbl 0972.37012 |
| [70] | P. Kahlig and J. Smítal, On a generalized Dhombres functional equa-tion, Aequationes Math. 62 (2001), 18-29. · Zbl 0994.39013 |
| [71] | P. Kahlig and J. Smítal, On a generalized Dhombres functional equa-tion. II, Math. Bohem. 127 (2002), 547-555. · Zbl 1007.39016 |
| [72] | J Smítal, Various notions of chaos, recent results, open problems, Real Anal. Exchange (2002), 26th Summer Symposium Conference, 81-85. · Zbl 1192.37016 |
| [73] | J. Smítal and M. Štefánková, Omega-chaos almost everywhere, Discrete Contin. Dyn. Syst. 9 (2003), 1323-1327. · Zbl 1041.37016 |
| [74] | F. Balibrea, L. Reich and J. Smítal, Iteration theory: dynamical systems and functional equations, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2003), 1627-1647. · Zbl 1056.37003 |
| [75] | F. Balibrea, B. Schweizer, A. Sklar and J. Smítal, Generalized specifica-tion property and distributional chaos, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2003), 1683-1694. · Zbl 1056.37006 |
| [76] | J. Smítal and M. Štefánková, Distributional chaos for triangular maps, Chaos Solitons Fractals 21 (2004), 1125-1128. · Zbl 1060.37037 |
| [77] | L. Reich, J. Smítal and M. Štefánková, The continuous solutions of a generalized Dhombres functional equation, Math. Bohem. 129 (2004), 399-410. · Zbl 1080.39505 |
| [78] | J. Smítal, Ten years of distributional chaos, Real Anal. Exchange (2004), 28th Summer Symposium Conference, 15-19. · Zbl 1063.37013 |
| [79] | F. Balibrea, J. Smítal and M. Štefánková, The three versions of distri-butional chaos, Chaos Solitons Fractals 23 (2005), 1581-1583. · Zbl 1069.37013 |
| [80] | L. Paganoni and J. Smítal, Strange distributionally chaotic triangular maps, Chaos Solitons Fractals 26 (2005), 581-589. · Zbl 1081.37005 |
| [81] | L. Reich, J. Smítal and M. Štefánková, The converse problem for a generalized Dhombres functional equation, Math. Bohem. 130 (2005), 301-308. · Zbl 1110.39014 |
| [82] | G. L. Forti, L. Paganoni and J. Smítal, Triangular maps with all periods and no infinite ω-limit set containing periodic points, Topology Appl. 153 (2005), 818-832. · Zbl 1176.37010 |
| [83] | J. Smítal, Dynamics of triangular maps -recent progress, Real Anal. Exchange (2005), 29th Summer Symposium Conference, 15-18. · Zbl 1096.37007 |
| [84] | L. Reich, J. Smítal and M. Štefánková, Local analytic solutions of the generalized Dhombres functional equation. I, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 214 (2005), 3-25. · Zbl 1117.39015 |
| [85] | L. Paganoni and J. Smítal, Strange distributionally chaotic triangular maps. II, Chaos Solitons Fractals 28 (2006), 1356-1365. · Zbl 1105.37008 |
| [86] | F. Balibrea and J. Smítal, A triangular map with homoclinic orbits and no infinite ω-limit set containing periodic points, Topology Appl. 153 (2006), 2092-2095. · Zbl 1094.37019 |
| [87] | J. Smítal, Topological entropy and distributional chaos, Real Anal. Ex-change (2006), 30th Summer Symposium Conference, 61-65. · Zbl 1117.37009 |
| [88] | L. Reich, J. Smítal and M. Štefánková, The holomorphic solutions of the generalized Dhombres functional equation, J. Math. Anal. Appl. 333 (2007), 880-888. · Zbl 1133.39019 |
| [89] | J. Smítal, Dynamical systems generated by piecewise continuous maps of the interval, Real Anal. Exchange (2007), 31st Summer Symposium Conference, 97-99. · Zbl 1152.37327 |
| [90] | L. Paganoni and J. Smítal, Strange distributionally chaotic triangular maps. III, Chaos Solitons Fractals 37 (2008), 517-524. · Zbl 1157.37312 |
| [91] | J. Smítal, Why it is important to understand dynamics of triangular maps?, J. Difference Equ. Appl. 14 (2008), 597-606. · Zbl 1146.37027 |
| [92] | J. Smítal, Dhombres type functional equations with non-trivial solu-tions, Real Anal. Exchange 33 (2008), 493-494. |
| [93] | J. Smítal and T. H. Steele, Stability of dynamical structures under per-turbation of the generating function, J. Difference Equ. Appl. 15 (2009), 77-86. · Zbl 1161.37017 |
| [94] | F. Balibrea and J. Smítal, Strong distributional chaos and minimal sets, Topology Appl. 156 (2009), 1673-1678. · Zbl 1175.37034 |
| [95] | L. Reich, J. Smítal and M. Štefánková, Local analytic solutions of the generalized Dhombres functional equation. II, J. Math. Anal. Appl. 355 (2009), 821-829. · Zbl 1190.39012 |
| [96] | L. Reich and J. Smítal, Functional equation of Dhombres type-a simple equation with many open problems, J. Difference Equ. Appl. 15 (2009), 1179-1191. · Zbl 1178.39034 |
| [97] | L. Obadalová and J. Smítal, Distributional chaos and irregular recur-rence, Nonlinear Anal. 72 (2010), 2190-2194. · Zbl 1180.37019 |
| [98] | F. Hofbauer, P. Raith and J. Smítal, The space of ω-limit sets of piecewise continuous maps of the interval, J. Difference Equ. Appl. 16 (2010), 275-290. · Zbl 1189.37047 |
| [99] | L. Reich and J. Smítal, On generalized Dhombres equations with non-constant polynomial solutions in the complex plane, Aequationes Math. 80 (2010), 201-208. · Zbl 1210.39026 |
| [100] | F. Balibrea, J. Smítal and M. Štefánková, A triangular map of type 2 ∞ with positive topological entropy on a minimal set, Nonlinear Anal. 74 (2011), 1690-1693. · Zbl 1213.37019 |
| [101] | F. Balibrea, J. Smítal and M. Štefánková, On open problems concerning distributional chaos for triangular maps, Nonlinear Anal. 74 (2011), 7342-7346. · Zbl 1223.37015 |
| [102] | L. Reich, J. Smítal and M. Štefánková, Functional equation of Dhombres type in the real case, Publ. Math. Debrecen 78 (2011), 659-673. · Zbl 1274.39040 |
| [103] | L. Obadalová and J. Smítal, Counterexamples to the open problem by Zhou and Feng on the minimal centre of attraction, Nonlinearity 25 (2012), 1443-1449. · Zbl 1243.37003 |
| [104] | L. Reich, J. Smítal and M. Štefánková, On generalized Dhombres equa-tions with non-constant rational solutions in the complex plane, J. Math. Anal. Appl. 399 (2013), 542-550. · Zbl 1304.39026 |
| [105] | L. Reich, J. Smítal and M. Štefánková, Singular solutions of the gen-eralized Dhombres functional equation, Results Math. 65 (2014). · Zbl 1311.39026 |
| [106] | F. Balibrea, J. Smítal and M. Štefánková, Dynamical systems generat-ing large sets of probability distribution functions, Chaos Solitons Frac-tals 67 (2014), 38-42. · Zbl 1349.37011 |
| [107] | J. Smítal and M. Štefánková, On regular solutions of the generalized Dhombres equation, Aequationes Math. 89 (2015), 57-61. · Zbl 1317.39029 |
| [108] | L. Reich, J. Smítal and M. Štefánková, On regular solutions of the generalized Dhombres equation II, Results Math. 67 (2015), 521-528. · Zbl 1386.39035 |
| [109] | J. Smítal and M. Štefánková, Generalized Dhombres functional equa-tion, in: “Developments in functional equations and related topics,” Springer Optim. Appl. 124 (2017), 297-303. · Zbl 1387.39015 |
| [110] | F. Balibrea, J. Smítal and M. Štefánková, On generic properties of nonautonomous dynamical systems, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 28 (2018), 1850102. Books by Jaroslav Smítal · Zbl 1395.37013 |
| [111] | J. Smítal and T. Šalát, Real Numbers for the 3rd year of Grammar Schools with a Focus on Mathematics (Slovak), SPN, Bratislava 1977, 112 pp. and (Czech), SPN, Praha 1977, 145 pp. |
| [112] | J. Smítal, Introduction to the Set Theory and Mathematical Logic I (Slovak), PÚMB, Bratislava 1978, 64 pp. |
| [113] | J. Smítal, Introduction to the Set Theory and Mathematical Logic II (Slovak) PÚMB Bratislava 1978, 51 pp. |
| [114] | J. Smítal, E. Gedeonová and Š. Znám, Introduction to Linear Algebra (Slovak), Comenius University, Bratislava 1978, 116 pp. |
| [115] | J. Smítal and E. Gedeonová, Linear Algebra (Slovak), Comenius Uni-versity, Bratislava 1981, 115 pp. |
| [116] | J. Smítal, On functions and functional equations (Slovak), Alfa, Bratislava 1984, 144 pp. English translation: Adam Hilger, Ltd., Bris-tol, 1988. Translated from Slovak by J. Dravecký. |
| [117] | T. Katriňák, M. Gavalec, E. Gedeonová and J. Smítal, Algebra and Theoretical Arithmetic I (Slovak), Alfa, Bratislava and SNTL, Praha 1985, 351 pp. 2nd Edition: Comenius University, Bratislava 1995. |
| [118] | T. Neubrunn and J. Smítal, Topics in Analysis. Functional Analysis and the Theory of Functions (Slovak), Comenius University, Bratislava 1985, 210 pp. |
| [119] | T. Šalát and J. Smítal, Set Theory (Slovak), Alfa, Bratislava and SNTL, Praha 1986, 224 pp. 2nd Edition: Comenius University, Bratislava 1995. |
| [120] | J. Smítal and T. Šalát, Sequences and Series for the 3rd year of Gram-mar Schools with a Focus on Mathematics (Czech), SPN, Praha 1986, 64 pp. and (Slovak), SPN, Bratislava 1987, 92 pp. Publications co-edited by Jaroslav Smítal |
| [121] | L. Reich, J. Smítal, G. Targonski (Eds.), Iteration theory, ECIT ’94. Proceedings of the European conference, Opava, Czech Republic, August 28-September 3, 1994., Grazer Math. Ber. 334 (1997), 261 p. · Zbl 0905.00063 |
| [122] | F. Balibrea, L. Reich, J. Smítal (Eds.), Dynamical systems and func-tional equations. Papers from the 13th European conference on iteration theory (ECIT 2000), Murcia, Spain, September 4-9, 2000., Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2003), no. 7, 1625-2012. · Zbl 1423.37005 |
| [123] | W. Förg-Rob, L. Gardini, D. Gronau, L. Reich, J. Smítal (Eds.), Iter-ation theory (ECIT ’04). Proceedings of the 15th European conference, Batschuns, Austria, August 29-September 5, 2004, Grazer Math. Ber. 350 (2006), 246 p. · Zbl 1132.39300 |
| [124] | G. L. Forti, D. Gronau, L. Paganoni, L. Reich, J. Smítal (Eds.), It-eration theory (ECIT ’06). Proceedings of the 16th European confer-ence, Gargnano, Italy, September 10-16, 2006, Grazer Math. Ber. 351 (2007), 194 p. · Zbl 1133.37001 |
| [125] | J. Smítal, Editorial [Special issue: European Conference on Iteration Theory 2016]. Held in Innsbruck, September 4-10, 2016. Special issue Ľ. Snoha edited by Marek Cezary Zdun and Jaroslav Smítal. J. Difference Equ. Appl. 24 (2018), no. 5, 655. Other references · Zbl 1390.00169 |
| [126] | S. J. Agronsky, A. M. Bruckner, J. G. Ceder and T. L. Pearson, The structure of ω-limit sets for continuous functions, Real Anal. Exchange 15 (1989-90), 483-510. · Zbl 0728.26006 |
| [127] | F. Balibrea, V. Jiménez López, The measure of scrambled sets: a sur-vey, Acta Univ. M. Belii Ser. Math. 7 (1999), 3-11. · Zbl 0967.37021 |
| [128] | L. Block, Simple periodic orbits of mappings of the interval, Trans. Amer. Math. Soc. 254 (1979), 391-398. · Zbl 0386.54025 |
| [129] | A. M. Bruckner, J. G. Ceder, M. Weiss, Uniform limits of Darboux functions, Colloq. Math. 15 (1966), 65-77. · Zbl 0138.28004 |
| [130] | A. M. Bruckner, J. Ceder, On the sum of Darboux functions, Proc. Amer. Math. Soc. 51 (1975), 97-102. · Zbl 0306.26002 |
| [131] | J. Dhombres, Applications associatives ou commutatives (French), C. R. Acad. Sci. Paris Sér. A-B 281 (1975), no. 19, Aii, A809-A812. · Zbl 0344.39009 |
| [132] | J. Doleželová-Hantáková, Z. Roth, S. Roth, On the weakest version of distributional chaos, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 26 (2016), no. 14, 1650235, 13 pp. · Zbl 1357.37012 |
| [133] | T. Downarowicz, Positive topological entropy implies chaos DC2, Proc. Amer. Math. Soc. 142 (2014), no. 1, 137-149. · Zbl 1304.37008 |
| [134] | H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory 1 (1967), 1-49. · Zbl 0146.28502 |
| [135] | I. Kan, A chaotic function possessing a scrambled set with positive Lebesgue measure, Proc. Amer. Math. Soc. 92 (1984), no. 1, 45-49. · Zbl 0592.26005 |
| [136] | H. Kestelman, On the functional equation f (x+y) = f (x)+f (y), Fund. Math. 34 (1947), 144-147. · Zbl 0032.02804 |
| [137] | P. E. Kloeden, On Sharkovsky’s cycle coexistence ordering, Bull. Aus-tral. Math. Soc. 20 (1979), no. 2, 171-177. · Zbl 0465.58022 |
| [138] | S. F. Kolyada, On dynamics of triangular maps of the square, Ergodic Theory Dynam. Systems 12 (1992), no. 4, 749-768. · Zbl 0784.58038 |
| [139] | S. Kolyada, Ľ. Snoha, S. Trofimchuk, Minimal sets of fibre-preserving maps in graph bundles, Math. Z. 278 (2014), no. 1-2, 575-614. · Zbl 1378.54036 |
| [140] | Z. Kominek, Some generalization of the theorem of S. Piccard, Uniw. Śląski w Katowicach -Prace Mat. 4 (1973), 31-33. · Zbl 0268.26003 |
| [141] | M. Kuczma, Problem P 35, Aequationes Math. 2 (1969), p. 378. |
| [142] | T. Y. Li, J. A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), no. 10, 985-992. · Zbl 0351.92021 |
| [143] | A. Ostrowski, Mathematische Miszellen. XIV: Über die Funktionalgle-ichung der Exponentialfunktion und verwandte Funktionalgleichungen (German), Jahresber. Deutsch. Math.-Verein. 38 (1929), 54-62. · JFM 55.0800.01 |
| [144] | S. Piccard, Sur des ensembles parfaits (French). Mém. Univ. Neuchâtel, vol. 16. Université de Neuchâtel, Secrétariat de l’Université, Neuchâtel, 1942. 172 pp. |
| [145] | R. Pikuła, On some notions of chaos in dimension zero, Colloq. Math. 107 (2007), no. 2, 167-177. · Zbl 1130.37327 |
| [146] | S. Ruette, Ľ. Snoha, For graph maps, one scrambled pair implies Li-Yorke chaos, Proc. Amer. Math. Soc. 142 (2014), no. 6, 2087-2100. · Zbl 1348.37068 |
| [147] | Ľ. Snoha, M. Štefánková, Professor Jaroslav Smítal 60 years old (Slo-vak), Obzory matematiky, fyziky a informatiky 31 (2002), no. 2, 59-61. |
| [148] | Ľ. Snoha, M. Štefánková, Professor Jaroslav Smítal 60 years old (Czech), Pokroky matematiky, fyziky a astronomie 47 (2002), no. 2, 171-173. |
| [149] | Ľ. Snoha (Ed.), Jaroslav Smítal: Doctor honoris causa of Matej Bel University in Banská Bystrica (Slovak), Belianum, Banská Bystrica, 2017, 24pp. |
| [150] | A. N. Šarkovskii, Attracting sets containing no cycles (Russian), Ukrain. Mat. Ž. 20 (1968), no. 1, 136-142. · Zbl 0174.54404 |
| [151] | A. N. Šarkovskii, Attractors of trajectories and their basins (Russian), Kiev, Naukova Dumka 2013. |
| [152] | Ľ. Snoha |
| [153] | M. Štefánková, Strong and weak distributional chaos, J. Difference Equ. Appl. 19 (2013), no. 1, 114-123. · Zbl 1278.37015 |
| [154] | M. Štefánková, The Sharkovsky program of classification of triangular maps -a survey, Topology Proc. 48 (2016), 135-150. · Zbl 1357.37014 |
| [155] | H. Wang, F. Lei, L. Wang, DC3 and Li-Yorke chaos, Appl. Math. Lett. 31 (2014), 29-33 · Zbl 1311.37027 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
