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2021 Topological Entropy of Free Semigroup Actions Generated by Proper Maps for Noncompact Subsets
Xiaoyi Xie, Dongkui Ma
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Taiwanese J. Math. Advance Publication 1-24 (2021). DOI: 10.11650/tjm/210903

Abstract

In this paper, we introduce three notions of topological entropy of a free semigroup action generated by proper maps for noncompact subsets, which extends the notions defined by Ju et al. [13] and Ma et al. [17]. By using the one-point compactification as a bridge, we study the relations of the entropies between two dynamical systems. We then introduce three skew-product transformations, and for a particular subset, the relationship between the upper capacity topological entropy of a free semigroup action generated by proper maps, and the upper capacity topological entropy of a skew-product transformation is given. As applications, we examine the multifractal spectrum of a locally compact separable metric space, and it is shown that the irregular set has full upper capacity topological entropy of a free semigroup action generated by proper maps.

Funding Statement

The work was supported by National Natural Science Foundation of China (grant no. 11771149).

Acknowledgments

The authors really appreciate the editor and referees' valuable remarks and suggestions that helped a lot.

Citation

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Xiaoyi Xie. Dongkui Ma. "Topological Entropy of Free Semigroup Actions Generated by Proper Maps for Noncompact Subsets." Taiwanese J. Math. Advance Publication 1 - 24, 2021. https://doi.org/10.11650/tjm/210903

Information

Published: 2021
First available in Project Euclid: 23 September 2021

Digital Object Identifier: 10.11650/tjm/210903

Subjects:
Primary: 37A35, 37B40

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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