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Moscow University Mathematics Bulletin

, Volume 74, Issue 3, pp 131–133 | Cite as

The Set of Lower Semi-Continuity Points of Topological Entropy of a Continuous One-Parametric Family of Dynamical Systems

  • A. N. VetokhinEmail author
Article

Abstract

The description of the set of lower semi-continuity points and the set of upper semi-continuity points of the topological entropy of the systems considered as a function on some parameter is obtained for a family of dynamical systems continuously dependent on parameter.

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References

  1. 1.
    A. B. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge Univ. Press, Cambridge, 1995; Faktorial, Moscow, 1999).CrossRefzbMATHGoogle Scholar
  2. 2.
    A. N. Vetokhin, “Typical Property of the Topological Entropy of Continuous Mappings of Compact Sets,” Diff. Uravn. 53 (4), 448 (2017) [Diff. Eq. 53 (4), 439 (2017)].MathSciNetzbMATHGoogle Scholar
  3. 3.
    M. V. Karpuk, “Structure of the Semicontinuity Sets of the Lyapunov Exponents of Linear Differential Systems Continuously Dependent on a Parameter,” Diff. Uravn., 51 (9), 1404 (2015) [Diff. Eq. 51 (10), 1397 (2015)].MathSciNetGoogle Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityLeninskie Gory, MoscowRussia
  2. 2.Bauman Moscow State Technical UniversityMoscowRussia

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