MATHEMATICS

On some properties of the local entropy of dynamical systems unwinded as a function of a point in the phase space

A. N. Vetokhin

Lomonosov Moscow State University, Leninskie Gory, 1, GSP-1, Moscow, 119991, Russia

Abstract: The article studies the nature of the dependence on the local entropy point of a non-autonomous dynamical system. It is proved that the local entropy is a function of the second Baire class on the phase space, and its set of lower semicontinuity points forms an everywhere dense set of type $G_\delta$. An autonomous dynamical system is constructed such that the set of above semicontinuity points of the local entropy of this system is empty.

Keywords: dynamical systems, local entropy, Baire classification of functions

UDC: 517.938.5

MSC: 37B02

Received: 10.01.2025
Accepted: 02.06.2025

DOI: 10.35634/vm250202

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