Advertisement

Mathematical Notes

, Volume 106, Issue 3–4, pp 327–333 | Cite as

The Exact Baire Class of Topological Entropy of Nonautonomous Dynamical Systems

  • A. N. Vetokhin
Article
  • 17 Downloads

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.

Keywords

nonautonomous dynamical system topological entropy Baire classification of functions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. L. Adler, A. G. Konheim, and M. H. McAndrew, “Topological entropy,” Trans. Amer. Math. Soc. 114 (2), 309–319 (1965).MathSciNetCrossRefGoogle Scholar
  2. 2.
    S. Kolyada and L’. Snoha, “Topological entropy of nonautonomous dynamical systems,” Random Comput. Dynam. 4 (2–3), 205–233 (1996).MathSciNetzbMATHGoogle Scholar
  3. 3.
    M. Misiurewicz, “Horseshoes for mappings of the interval,” Bull. Acad. Polon. Sci. Se´ r. Sci. Math. 27 (2), 167–169 (1979).MathSciNetzbMATHGoogle Scholar
  4. 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)].MathSciNetzbMATHGoogle Scholar
  5. 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. 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. 7.
    F. Hausdorff, Grundzüge der Mengenlehre (Veit & Comp., Leipzig, 1914; ONTI, Moscow, (1937).zbMATHGoogle Scholar
  8. 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)].MathSciNetzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • A. N. Vetokhin
    • 1
    • 2
  1. 1.Department of Mechanics and MathematicsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Bauman Moscow Higher Technical SchoolMoscowRussia

Personalised recommendations