Typical property of the topological entropy of continuous mappings of compact sets
- Authors: Vetokhin A.N.1
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Affiliations:
- Russian State University of Tourism and Service
- Issue: Vol 53, No 4 (2017)
- Pages: 439-444
- Section: Ordinary Differential Equations
- URL: https://journal-vniispk.ru/0012-2661/article/view/154335
- DOI: https://doi.org/10.1134/S0012266117040024
- ID: 154335
Cite item
Abstract
We show that the topological entropy viewed as a functional on the space of continuous mappings of a metric compact set into itself with the uniform topology is a function of the second Baire class and is lower semicontinuous at a Baire typical point. In particular, we show that the topological entropy is zero at a Baire typical point of the space of continuous mappings of the Baire space of sequences of zeros and units.
About the authors
A. N. Vetokhin
Russian State University of Tourism and Service
Author for correspondence.
Email: anveto27@yandex.ru
Russian Federation, Cherkizovo, Moscow Region, 141221
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