Variational principle for topological pressures on subsets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:424

Article

Tang, Xinjia¹  Cheng, Wen-Chiao²  Zhao, Yun¹ 

[1] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China

[2] Chinese Culture Univ, Dept Appl Math, Taipei 11114, Taiwan

关键词: Measure-theoretic pressure;    Variational principle;    Borel probability measure;    Topological pressure;   

DOI  :  10.1016/j.jmaa.2014.11.066

来源: Elsevier

【 摘 要 】

This paper studies the relations between Pesin-Pitskel topological pressure on an arbitrary subset and measure theoretic pressure of Borel probability measures, which extends Feng and Huang's recent result on entropies [13] for pressures. More precisely, this paper defines the measure theoretic pressure P-mu(T, f) for any Borel probability measure, and shows that P-B(T, f, K) = sup{P-mu(T, f) : mu is an element of M(X), (mu)(K) = 1}, where M(X) is the space of all Borel probability measures, K subset of X is a non-empty compact subset and P-B(T, f, K) is the Pesin-Pitskel topological pressure on K. Furthermore, if Z subset of X is an analytic subset, then P-B(T, f, Z) = sup{P-B(T, f, K) K subset of Z is compact}. This paper also shows that Pesin-Pitskel topological pressure can be determined by the measure theoretic pressure. (C) 2014 Elsevier Inc. All rights reserved.

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