Position Professor, Head of the Mathematical Institute
Address Mathematical Institute
Silesian University in Opava
Na Rybnicku 1
746 01 Opava, Czech Republic
Phone +420 553 684 660
Fax +420 553 684 680
E-mail

Curriculum

Research

Discrete dynamical systems. Real analysis. Functional equations.

List of publications

  1. On sequences of Darboux functions, PhD thesis, (1970). (Thesis is the collection of papers [10], [11] a [13].)
  2. On additive and convex functions, habilitation thesis, (1973). (Thesis is the collection of papers [8], [15], [17] a [18].)
  3. On some problems in the theory of real functions, DrSc. thesis (1983). (Thesis is the collection of papers [13], [15], [16], [17], [20], [27] , [28], [30], [31] a [33].)
  4. On the structure of the space Lp, Acta Fac. RNUC 10 (1966), 43 - 48. (Czech) (MR 34#3292, RI 6B (1967) 586, Zblt. 171.334)
  5. (with T. Salat) Bemerkung zur Approximation der stetige Funktionen durch Polynom, Acta Fac. RNUC 16 (1967), 43 - 47. (MR 38#4864, R× 7B (1969) 92, Zblt 172.78)
  6. (with T. Neubrunn and T. Salat) On certain properties charcterizing locally separable metric spaces, Casopis pest. matem. 92 (1967), 157 - 161. (MR 36#5891, RZ 10A (1967) 369, Zblt 171.437)
  7. (with T. Neubrunn and T. Salat) On the structure of the space M(0,1), Rev. Roum. Math. Pures Appl. 13, 377 - 386, (1968). (MR 38#2592, RZ 12B (1968) 65, Zblt 174.439)
  8. On the functional equation f(x+y)=f(x)+f(y), Rev. Roum. Math. Pures Appl. 13 (1968), 555 - 561. (MR38#2475, RZ 4B (1969) 7, Zblt 165.500)
  9. (with P. Kostyrko and T.Salat) Remarks on the theory of real functions, Acta Fac. RNUC 20 (1969), 81 - 89. (MR 42#7852, RZ 3B (1971) 55, Zblt 2O8.324)
  10. On a problem concerning uniform limits of Darboux functions, Colloquium Math 23 (1971), 115 - 116. (MR 46#306, RZ 2B (1972) 73, Zblt 219.151)
  11. On approximation of Baire functons by Darboux functions, Czech. Math. J. 21 (96) (1971), 418 - 423. (MR 45#470, RZ 1B (1972) 85, Zblt 219.150)
  12. Some remarks on ratio sets of sets of natural numbers, Acta Fac. RNUC 25 (1971), 93 - 99. (MR51#10279, RZ 6A (1972) 123, Zblt 228.10036)
  13. Some characterizations of Darboux continuity Matemat. ˙asop. 22 (1972), 59 - 70. (MR46#1974, RZ 8B (1972) 40, Zblt 228.26007)
  14. A note on the class M2, Acta Fac. RNUC 27 (1972), 97 - 99. (MR47#8778, RZ 6B (1973) 53, Zblt 248.26004)
  15. On boundedness and discontinuity of additive functions, Fundamenta Math. 76 (1972), 245 - 253. (MR47#9109, RZ 5B (1973) 10, Zblt 246.26008)
  16. Characteristic types of convergence for certain classes of Darboux Baire l functions, Mat. casop. 23 (1973), 115 - 116. (MR48#6331, RZ 11B (1973) 47, Zblt 271.26004)
  17. A necessary and sufficient condition for continuity of additive functions, Czechoslovak Math. J. 26 (101), 171 - 173, (1976). (MR 53#6138, RZ 2B (1977) 1, Zblt. 332.26005)
  18. On convex functions bounded below, Aequationes Math. 14 (1976), 345 - 350.(MR 55#3189, RZ 2B (1977) 49, Zblt 324.26006)
  19. On the sum of continuous and Darboux functions, Proc. Amer. Math. Soc. 60 (1976), 183 - 184. (MR 54#5403, RZ 10B (1977) 71, Zblt 339.26006)
  20. (with M. Kuczma) On measures connected with the Cauchy equation, Aequationes Math. 14 (1976), 421 - 428. (MR 53#13502, RZ 11B (1976) 962, Zblt 326.39007)
  21. (with Salat) Remarks on two generalizations of the notion of continuity, Acta Fac. RNUC 36 (1980), 115 - 119. (MR 83a:26010, RZ 9B (1981) 22, Zblt 531.26001)
  22. (with P. Kostyrko, T. Neubrunn and T. Salat) Remarks on the theory of real functions, Acta Fac. RNUC 36 (1980), 7 - 23. (MR 83a:26008, RZ 9B (1981) 22)
  23. (with P. Kostyrko, T. Neubrunn and T. Salat) On symmetric and symmetrically continuous functions, Real Analysis Exchange 6 (1980), 68 - 76. ISSN 0147-1937 (MR 82c: 26005, RZ 1B (1982) 60, Zblt 459.26001)
  24. (with E. Stanova) On almost ontinuous functions, Acta Math. UC 37 (1980), 147 - 156. (MR84b: 54026, RZ 5A (1982) 496, Zblt 554.26003)
  25. (with L. Snoha) Generalization of a theorem of S. Picard, Acte Math. UC 37 (1980), 173 - 181. (MR 84b: 26012, RZ 5B (1982) 68, Zblt 526.26005)
  26. Iterates of piecewise monotonic continuous functions, Math. Slovaca 32 (1982), 143 - 146. ISSN 0025-5173 (MR 83k: 58068, RZ 9B (1982) 45, Zblt 498.26003)
  27. (with K. Smitalova) Structural stability of non-chaotic difference equations, J. Math. Anal. Appl. 90 (1982), 1 - 11. ISSN 0022-247X (MR 84d: 58046, RZ 5B (1983) 230, Zblt 505.39004)
  28. A chaotic function with some extremal properties, Proc. Amer. Math. Soc. 87 (1983), 54 - 56. ISSN 0002-9939 (MR 84h: 26008, RZ 7B (1983) 35, Zblt 555.26003)
  29. (with E. Kubackova) On weakly closed functions, Acta Math. UC 42 - 43 (1983), 115 - 120. (MR85f: 54026, RZ 11B (1985) 39, Zblt 597.54014)
  30. A chaotic function with a scrambled set of positive Lebesgue measure, Proc. Amer. Math. Soc. 92 (1984), 50 - 54. ISSN 0002-9939 (MR 86b: 26009, RZ 10B (1985) 43, Zblt 592.26006)
  31. Erratum to the paper: Smital - Smitalova, Structural stability of non-chaotic difference equations, J. Math. Anal. Appl. 101 (1984), 324. ISSN 0022-247X (MR 85f: 58065, Zblt 596.39004)
  32. (with K. Neubrunnova) Stability of typical continuous functions with respect to some properties of their iterates, Proc. Amer. Math. Soc. 90 (1984), 321 - 324. ISSN 0002-9939 (MR 85g: 54040, RZ 9B (1985) 34, Zblt 529.54038)
  33. On a problem of Acz?l and Erdos concerning Hamel bases, Aequationes Math. 28 (1985), 135 - 137. ISSN 0001-9054 (MR 86e:04004 RZ 7A (1985) 131, Zblt 558.12011)
  34. Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297 (1986), 269 - 282. ISSN 0002-9947 (MR 87m: 58107, RZ 3B (1987) 1119, Zblt 639.54029)
  35. (with K. Jankova), A characterization of chaos, Bull. Austral. Math. Soc. 34 (1986), 283 - 292. ISSN 0004-9727 (MR 87k: 58178, RZ 6B (1987) 1036, Zblt 577.54041)
  36. (with M. Misiurewicz) Smooth chaotic mappings with zero topological entropy, Ergodic Theory & Dynam. Systems 8 (1988), 421 - 424. ISSN 0143-3857 (MR 90a:58118 RZ 4B (1989) 1271, Zblt 689.58028)
  37. On Darboux solutions of the Euler's equation, Aequationes Math. 37 (1989), 279 - 231. ISSN 0001-9054 (MR 90j: 39007, Zblt 674.39006)
  38. (with M. Kuchta) Two point scrambled set implies chaos, World Sci. Publ. Singapore 1989 (Proceedings of the European Conference of Iteration Theory, Spain 1987), 427 - 430. ISBN: 981-02-0041-2 (MR 91j: 58112, RZ 12B (1991) 372)
  39. (with D. Preiss) A characterization of non-chaotic continuous maps of the interval stable under small perturbations, Trans. Amer. Math. Soc. 313 (1989), 687 - 696. ISSN 0002-9947 (MR 90f: 58100, Zblt 698.58033)
  40. (with K. Jankova) A theorem of Sharkovskii characterizing continuous maps of the interval with zero topological entropy, Math. Slovaca 39 (1989), 261 - 265. ISSN 0025-5173 (MR 90m: 58165, RZ 12B (1989) 1153, Zblt 686.26002)
  41. (with V. V. Fedorenko and A. N. Sharkovskii) Charakterizacia nekotorych klassov otobraženij intervala s nulevoj topologičeskoj entropiej, Preprint 89.58, Inst. Mat. AN USSR, Kiev 1989, 18 stran. (MR 90m: 58141, RZ 1B (1990) 865)
  42. (with V. V. Fedorenko and A. N. Sharkovskii) Characterizations of weakly chaotic maps of the interval, Proc. Amer. Math. Soc. 110 (1990), 141-148 (new version of paper [41]). ISSN 0002-9939 (MR91a: 58148, RZ 8B (1991) 974, Zblt 728.26008)
  43. (with N. Franzova) Positive sequence topological entropy characterizes chaotic maps, Proc. Amer. Math. Soc. 112 (1991), 1083 - 1086. ISSN 0002-9939 (MR 91j: 58107, Zblt 735.26005)
  44. (with V. V. Fedorenko), Maps of the interval Ljapunov stable on the set of nonwandering points, Acta Math. Univ. Comen. 60.1 (1991), 11 - 14. ISSN 0862-9544 (MR 92g: 58063, RZ11B (1991) 283, Zblt 736.58027)
  45. Solution of a problem by Prof. Targonski concerning semiconjugated maps,Proc. European Conference on Iteration Theory , Batschuns 1989, World Sci. Publ., River Edge, NJ, 1991, 382 - 383. ISBN: 981-02-0611-9 (MR 93e:58001)
  46. (with A. M. Bruckner) The structure of omega-limit sets for continuous maps of the interval, Mathematica Bohemica 117 (1992), 42 - 47. ISSN 0862-7959 (MR 93a: 26002, Zblt. 762.26003)
  47. (with A. M. Bruckner) A characterization of omega-limit sets of maps of the interval with zero topological entropy, Ergodic Theory & Dynam. Systems 13 (1993), 7 - 19. ISSN 0143-3857 (MR: 94k:26006, Zblt. 788.58021)
  48. (with E. M. Coven) Entropy minimality, Acta Math. Univ. Comen. 62 (1993), 117 - 121. ISSN 0862-9544 (MR 94g: 58120, Zblt 950.39516)
  49. (with F. Balibrea) A chaotic continuous map generates all probability distributions, J. Math. Anal. Appl. 180 (1993), 587 - 598. ISSN 0022-247X (MR: 94j:58099, Zblt. 794.60009)
  50. (with B. Schweizer) Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc. 344 (1994), 737 - 854. ISSN 0002-9947 (MR: 94k:58091, Zblt 812.58062))
  51. (with G. L. Forti and L. Paganoni) Strange triangular maps of the square, Bulletin Austral. Math. Soc. 51 (1995), 395 - 415. (Cf. also Preprint 20/1993, 20 pp., Universita Degli Studi di Milano.) ISSN 0004-9727 (MR 96d:54036, Zblt 832.54033)
  52. (with P. Kahlig) On the solutions of a functional equation of Dhombres, Results in Mathematics 27 (1995), 362 - 367. ISSN 0378-6218 (Zblt 860.39030, MR 96e:39010)
  53. (with K. Jankova) Generically there are no chaotic maps with random perturbations, International J. of Bifurcation and Chaos 5 (1995), 1375 - 1378. ISSN 0218-1274. (MR 96k:58196)
  54. (with F. Balibrea) A characterization of the set for continuous maps of the interval with zero topological entropy (abstract of [54]), International J. of Bifurcation and Chaos 5 (1995), 1433 - 1435. ISSN 0218-1274. (MR 97b:58048)
  55. (with A. Blokh, A. M. Bruckner, P. Humke), The space of omega-limit sets of a continuous map of the interval. MSRI Preprint No. 063-94, 19 pp, Mathematical Sciences Research Institute, Berkeley, CA 1994. Trans. Amer. Math. Soc.148 (1996), pp. 1357 - 1372.ISSN 0002-9947 (MR 96j:58089, Zbl 860.54036)
  56. (with F. Balibrea) A characterization of the set for continuous maps of the interval with zero topological entropy. Real Analysis Exchange 21(2) (1995/96), pp. 622 - 628. ISSN 0147-1937 (MR 97g:58097, Zbl 879.26017)
  57. (with P. Kahlig) On a parametric functional equation of Dhombres type, Aequationes Mathematicae 56 (1998), 63-68. ISSN 0001-9054 (MR 99j:39019, Zbl 915.39011)
  58. (with Ll. Alseda and M. Chas) On the structure of the omega-limit sets for continuous maps of the interval, Int. J. Bifurc. Chaos 9 (1999), 1719 - 1729. ISSN 0218-1274 (MR 2000i:37047)
  59. (with G.-L. Forti and L. Paganoni) Dynamics of homeomorphisms on minimal sets generated by triangular mappings. Bull. Austral. Math. Soc. 59 (1999), 1 - 20. ISSN 0004-9727 (MR 99m:54029)
  60. (with D. Pokluda) An omega-limit set universal function on [0,1], Real Analysis Exchange 24 (1998/99), 109 - 110. ISSN 0147-1937
  61. (with A. Sklar) Distributional chaos on compact metric spaces via specification properties, J. Math. Anal. Appl. 241 (2000), 181 - 188. ISSN 0022-247X (MR 2000k:37021)
  62. (with D. Pokluda) A "universal" dynamical system generated by a continuous map of the interval, Proc. Amer. Math. Soc., 128 (2000), 3047 - 3056. ISSN 0002-9939.
  63. (with V. Jimenez Lopez) Two counterexamples to a conjecture by Agronsky and Ceder, Acta Math. Hung. 88 (2000), 193-204. ISSN 0236-5294.
  64. P. Kahlig and J. Smital, On a generalized Dhombres functional equation, Aequationes Mathematicae 62 (2001) 18 - 29. ISSN 0001-9054.
  65. V. Jimenez Lopez (Univ. Murcia, Spain) and J. Smital, On omega-limit sets for triangular mappings, Fundamenta Mathematicae 167 (2001), 1 - 15. ISSN 0016-2736.
  66. B. Schweizer, A. Sklar and J. Smital, Distributional (and other) chaos and its measurement, Real Analysis Exchange 26 (2000/01), 495 - 524. ISSN 0147-1937.
  67. J. Smital and M. Stefankova, Strongly omega-chaotic mappings of the interval, Real Analysis Exchange 27(1) 2001/2002, 25th Summer Symposium Conference Report, 43 - 46. ISSN 0147-1937
  68. P. Kahlig (University of Vienna) and J. Smital, On a generalized Dhombres functional equation II. Math. Bohem. 127 (2002), 547-555. ISSN 0862-7959.
  69. J. Smital and M. Stefankova, Omega-chaos almost everywhere, Discrete and Continuous Dynamical Systems 9 (2003), 1323 - 1327.
  70. F. Balibrea, B. Schweizer, A. Sklar and J. Smital, Generalized specification property and distributional chaos. Internat. J. Bifur. Chaos 13 (2003), 1683 - 1694.
  71. F. Balibrea, L. Reich and J. Smital, Iteration Theory: Dynamical Systems and functional equations, Internat. J. Bifur. Chaos 13 (2003), 1627 - 1647.
  72. J. Smital, Triangulae maps with zero topological entropy, Summer Symposium 2003 (2004), 193 - 194. ISSN 0147-1937
  73. J. Smital and M. Stefankova, Distributional chaos for triangular maps, Chaos, Solitons and Fractals 21 (2004), 1125 - 1128.
  74. L. Reich, J. Smital and M. Stefankova, The continuous solutions of a generalized Dhombres functional equation, Math. Boh. 129 (2004), 399 - 410.
  75. F. Balibrea, J. Smital and M. Stefankova, The three versions of distributional chaos, Chaos, Solitons and Fractals 23 (2005), 1581 - 1583.
  76. L. Paganoni and J. Smital, Strange distributionally chaotic triangular maps, Chaos, Solitons and Fractals 26 (2005), 581 - 589.
  77. L. Reich, J. Smital and M. Stefankova, The converse problem for a generalized Dhombres functional equation, Math. Bohemica 130 (2005), 301 - 308.
  78. G.-L. Forti, L. Paganoni and J. Smital, Triangular maps with all periods and no infinite omega-limit set containing periodic points, Topology Appl. 153 (2005), 818 - 832.
  79. L. Paganoni and J. Smital, Strange distributionally chaotic maps II, Chaos, Solitons and Fractals 28 (2006), 1356 - 1365.
  80. F. Balibrea and J. Smítal, A triangular map with homoclinic orbit and no infinite omega-limit set containing periodic points, Topology Appl., 153 (2006), 2092 - 2103.
  81. L. Reich, J. Smital and M. Stefankova, Local analytic solutions of the generalized Dhombres functional equation I, Sitzungsberichte Oesterreich. Akad. Wiss. Abt. II, 214 (2006), 3 - 25.
  82. L. Reich, J. Smítal and M. Štefánková, The holomorphic solutions of the generalized Dhombres functional equation, J. Math. Anal. Appl. 333 (2007), 880 - 888. ISSN 0022-247X
  83. J. Smítal, Topological entropy and distributional chaos, Real Analysis Exchange, Summer Symposium 2006 (2007), 61 - 66.
  84. L. Paganoni and J. Smítal, Strange distributionally chaotic triangular maps III, Chaos, Solitons & Fractals 37 (2008), 517 - 524.
  85. J. Smítal, Why it is important to understant dynamics of triangular maps?, J. Difference Equations Appl. 14 (2008), 597 - 606.
  86. J. Smítal and T. H. Steele, Stability of dynamical structure under perturbation of the generating function, J. Difference Equations Appl. 15 (2009), 77 - 89.
  87. L. Reich, J. Smítal and M. Štefánková, Locally analytic solutions of the generalized Dhombres functional equation II, J. Math. Anal. Appl. 355 (2009), 821 - 829.
  88. F. Balibrea, J. Smítal, Strong distrinutional chaos and minimal sets, Topology Appl. 156 (2009), 1673 - 1678.
  89. L. Reich and J. Smítal, Functional equation of Dhombres type - a simple equation with many open problems, J. Difference Equations Appl. 15 (2009), 1179 - 1191.
  90. L. Obadalová and J. Smítal, Distributional chaos and irregular recurrence, Nonlin Anal A - Theor Meth Appl 72 (2010), 2190 - 2194. ISSN 0362-546X
  91. F. Hofbauer, P. Raith and J. Smítal, The space of omega-limit sets of piecewise continuous maps of the interval, J. Difference Equations Appl. 16 (2010), 275 - 290.
  92. L. Reich and J. Smítal, On generalized Dhombres equation with nonconstant polynomial solutions in the complex plane, Aequationes Math. 80 (2010), 201 - 208.
  93. F. Balibrea, J. Smítal and M. Štefánková, A triangular map of type 2 to infinity with positive topological entropy on a minimal set, Nonlin Anal A - Theor Meth Appl 74 (2011), 1690 - 1693.
  94. L. Reich, J. Smítal and M. Štefánková, Functional equation of Dhombres type in the real case, Publ Math Debrecen 78 (2011), 659 - 673.
  95. F. Balibrea, J. Smítal and M. Štefánková, On open problems concerning distributional chaos for triangular maps, Nonlin. Anal. A: Theory, Methods Appl. 74 (2011), 7342 - 7346.

Textbooks

  1. Introduction to the theory of real functions, Matematicke obzory 3 (1973), 21-36. (Slovak)
  2. (with T. Salat) Real Numbers, SPN Bratislava (1977), 112 pp. (Slovak)
  3. Introduction to the Set Theory and Mathematical Logic I, PÚMB, Bratislava 1978, 64 pp. (Slovak)
  4. Introduction to the Set Theory and Mathematical Logic II, PÚMB Bratislava 1978, 51 pp. (Slovak)
  5. Introduction to Linear Algebra, Comenius University, Bratislava 1978, 116 pp. (Slovak)
  6. (with E. Gedeonova) Linear Algebra, Comenius University, Bratislava, 1981, 115 pp. (Slovak)
  7. (with T. Katrinak, M. Gavalec and E. Gedeonova) Algebra and Theoretical Arithmetic I, Bratislava, Alfa 1985, 351 pp. (Slovak) MR 88i: 00001. 2nd Edition: Comenius University, Bratislava, 1995.
  8. (with T. Neubrunn) Topics in Analysis, Comenius University, Bratislava 1986, 220 pp. (Slovak)
  9. (with T. Salat) Set Theory, Alfa, Bratislava 1986, 224 pp. (Slovak) 2nd Edition: Comenius University, Bratislava, 1995.
  10. (with T. Salat) Sequences and Series, SPN Praha 1986, 64 stran. (Czech)
  11. On functions and functional equations, A. HILGER, Bristol - Philadelphia 1988, viii + 155 pp., ISBN 0-85274-418-8 (MR 90c: 39001, Zblt 644.39002).