Q-entropy for general topological dynamical systems

Yun Zhao; Wen-Chiao Cheng; Chih-Chang Ho

doi:10.3934/dcds.2019086

Article Contents

2019, Volume 39, Issue 4: 2059-2075. Doi: 10.3934/dcds.2019086

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$ L^p $

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Q-entropy for general topological dynamical systems

1.
School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, China
2.
Center for Dynamical Systems and Differential Equation, Soochow University, Suzhou 215006, Jiangsu, China
3.
Department of Applied Mathematics, Chinese Culture University, Yangmingshan, Taipei, 11114, Taiwan

* Corresponding author: Chih-Chang Ho
* Corresponding author: Chih-Chang Ho

Received: March 31, 2018

Revised: August 31, 2018

Published: January 2019

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Abstract

The aim of this paper is to extend the $ q $-entropy from symbolic systems to a general topological dynamical system. Using a (weak) Gibbs measure as the reference measure, this paper defines $ q $-topological entropy and $ q $-metric entropy, then studies basic properties of these entropies. In particular, this paper describes the relations between $ q $-topological entropy and topological pressure for almost additive potentials, and the relations between $ q $-metric entropy and local metric entropy. Although these relations are quite similar to that described in [19], the methods used here need more techniques from the theory of thermodynamic formalism with almost additive potentials.

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Mathematics Subject Classification: Primary: 37D35, 37C45; Secondary: 28D20.

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References

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