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2014 TOPOLOGICAL ENTROPY OF PROPER MAP
Dongkui Ma, Bin Cai
Taiwanese J. Math. 18(4): 1219-1241 (2014). DOI: 10.11650/tjm.18.2014.3339

Abstract

By using the Carathéodory-Pesin structure (C-P structure), the topological entropy on the whole space introduced for a proper map, is generalized to the cases of arbitrary subset, i.e., we introduce three notions of topological entropy. Some of the properties of these notions are provided. As some applications, for the proper map of locally compact separable metric space, we prove the following variational principles: (1) The upper capacity topological entropy on any subset and the minimum of the Bowen-Dinaburg entropies always coincide; (2) For any invariant probability measure, the measure-theoretic entropy and the infimum of the topological entropies on all sets which are of full measures always coincide; (3) The relationship between the topological entropies of level sets of the ergodic average of some continuous functions and the measure-theoretic entropies are given. These are the extensions of results of Patrão and Pesin, etc.

Citation

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Dongkui Ma. Bin Cai. "TOPOLOGICAL ENTROPY OF PROPER MAP." Taiwanese J. Math. 18 (4) 1219 - 1241, 2014. https://doi.org/10.11650/tjm.18.2014.3339

Information

Published: 2014
First available in Project Euclid: 10 July 2017

zbMATH: 1357.37008
MathSciNet: MR3245439
Digital Object Identifier: 10.11650/tjm.18.2014.3339

Subjects:
Primary: 37A35, 37B40, 37C45

Rights: Copyright © 2014 The Mathematical Society of the Republic of China

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Vol.18 • No. 4 • 2014
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