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
A. B. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge Univ. Press, Cambridge, 1995; Faktorial, Moscow, 1999).
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)].
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)].
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Russian Text © The Author(s). 2019. published in Vestnik Moskovskogo Universiteta. Matematika. Mekhanika. 2019. Vol. 74, No. 3, pp. 69–71.
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Vetokhin, A.N. The Set of Lower Semi-Continuity Points of Topological Entropy of a Continuous One-Parametric Family of Dynamical Systems. Moscow Univ. Math. Bull. 74, 131–133 (2019). https://doi.org/10.3103/S0027132219030069
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DOI: https://doi.org/10.3103/S0027132219030069