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Differential Equations

, Volume 55, Issue 8, pp 1118–1119 | Cite as

Family of Dynamical Systems Whose Topological Entropy Is Nowhere Upper Semicontinuous

  • A. N. VetokhinEmail author
Short Communications
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Abstract

We construct a continuous family of continuous mappings of a compact metric space such that the topological entropy of these mappings as a function of the parameter is nowhere upper semicontinuous.

References

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    Adler, R.L., Konheim, A.G., and McAndrew, M.H., Topological entropy, Trans. Amer. Math. Soc., 1965, vol. 114, no. 2, pp. 309–319.MathSciNetCrossRefzbMATHGoogle Scholar
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    Vetokhin, A.N., Typical property of the topological entropy of continuous mappings of compact sets, Differ. Equations, 2017, vol. 53, no. 4, pp. 439–444.MathSciNetCrossRefzbMATHGoogle Scholar
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    Katok, A. and Hasselblatt, B., Introduction to the Modern Theory of Dynamical Systems, Cambridge: Cambridge Univ., 1995. Translated under the title Vvedenie v sovremennuyu teoriyu dinamicheskikh sistem, Moscow: Faktorial, 1999.CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Bauman Moscow State Technical UniversityMoscowRussia

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