Abstract
We prove that the lower topological entropy considered as a function on the space of sequences of continuous self–maps of a metric compact space belongs to the second Baire class and the upper one belongs to the fourth Baire class.
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References
A. N. Vetokhiri, “Typical Property of the Topological Entropy of Continuous Mappings of Compact Sets,” Diff. Uravn. 53 (4), 448 (2017) [Differential Equations 53 (4), 439 (2017)].
S. Kolyada arid L. Srioha, “Topological Entropy of Nori–Autonomous Dynamical Systems,” Random arid Comput. Dynamics, No. 4, 205 (1996).
A. B. Katok arid B. Hasselblatt, Introduction to the Modem Theory of Dynamical Systems (Cambridge University Press, N.Y., Melbourne, Madrid, 1995; Factorial, Moscow, 1999).
F. Hausdorff, Set Theory (von Veit, Leipzig, 1914; ONTI, Moscow, 1937).
E. G. Arinysh, “On Generalization of a Theorem of Baire,” Uspekhi Matem. Nauk 8 (3), 105 (1953).
M. V. Karpuk, “Structure of the Semicoritiriuity Sets of the Lyapuriov Exponents of Linear Differential Systems Continuously Depending on a Parameter,” Diff. Uravn. 51 (10), 1404 (2015) [Differential Equations, 51 (10), 1397 (2015)].
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Original Russian Text © A.A. Astrelina, 2018, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2018, Vol. 73, No. 5, pp. 64–67.
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Astrelina, A.A. The Baire Class of Topological Entropy of Non–Autonomous Dynamical Systems. Moscow Univ. Math. Bull. 73, 203–206 (2018). https://doi.org/10.3103/S0027132218050078
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DOI: https://doi.org/10.3103/S0027132218050078