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The Exact Baire Class of Topological Entropy of Nonautonomous Dynamical Systems

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Abstract

We consider a parametric family of nonautonomous dynamical systems continuously depending on a parameter from some metric space. For any such family, the topological entropy of its dynamical systems is studied as a function of the parameter from the point of view of the Baire classification of functions.

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References

  1. R. L. Adler, A. G. Konheim, and M. H. McAndrew, “Topological entropy,” Trans. Amer. Math. Soc. 114 (2), 309–319 (1965).

    Article  MathSciNet  Google Scholar 

  2. S. Kolyada and L’. Snoha, “Topological entropy of nonautonomous dynamical systems,” Random Comput. Dynam. 4 (2–3), 205–233 (1996).

    MathSciNet  MATH  Google Scholar 

  3. M. Misiurewicz, “Horseshoes for mappings of the interval,” Bull. Acad. Polon. Sci. Se´ r. Sci. Math. 27 (2), 167–169 (1979).

    MathSciNet  MATH  Google Scholar 

  4. A. N. Vetokhin, “Typical property of the topological entropy of continuous mappings of compact sets,” Differ. Uravn. 53 (6), 448–453 (2017) [Differ. Equations 53 (4), 439–444 (2017)].

    MathSciNet  MATH  Google Scholar 

  5. A. N. Vetokhin, “The topological entropy on a space of homeomorphisms does not belong to the first Baire class,” Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 2, 44–48 (2016) [Moscow Univ. Math. Bull. 71 (2), 75–78 (2016)].

    Google Scholar 

  6. A. A. Astrelina, “Baire class of topological entropy of nonautonomous dynamical systems,” Vestnik Moskov. Univ. Ser. IMat.Mekh., No. 5, 64–67 (2018) [Moscow Univ.Math. Bull. 73 (5), 203–206 (2018)].

    Google Scholar 

  7. F. Hausdorff, Grundzüge der Mengenlehre (Veit & Comp., Leipzig, 1914; ONTI, Moscow, (1937).

    MATH  Google Scholar 

  8. A. N. Vetokhin, “The Baire class of maximal lower semicontinuous minorants of Lyapunov exponents,” Differ. Uravn. 34 (10), 1313–1317 (1998) [Differ. Equations 34 (10), 1313–1317 (1998)].

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991, Russia

    A. N. Vetokhin

  2. Bauman Moscow Higher Technical School, Moscow, 105005, Russia

    A. N. Vetokhin

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  1. A. N. Vetokhin
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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 3, pp. 333–340.

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Vetokhin, A.N. The Exact Baire Class of Topological Entropy of Nonautonomous Dynamical Systems. Math Notes 106, 327–333 (2019). https://doi.org/10.1134/S0001434619090025

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  • DOI: https://doi.org/10.1134/S0001434619090025

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