Variational Principle for Topological Pressure on Subsets of Free Semigroup Actions

We investigate the relations between Pesin-Pitskel topological pressure on an arbitrary subset and measure-theoretic pressure of Borel probability measures for finitely generated semigroup actions. Let ( X , ) be a system, where X is a compact metric space and is a finite family of continuous maps o...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 37; no. 9; pp. 1401 - 1414
Main Authors Zhong, Xing Fu, Chen, Zhi Jing
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.09.2021
Springer Nature B.V
Subjects
Continuity (mathematics)
Mathematics
Mathematics and Statistics
Metric space
Semigroups
Topology
variational principle
37B40
semigroup of continuous maps
37A35
37C45
measure-theoretic pressure
Topological pressure
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Summary:We investigate the relations between Pesin-Pitskel topological pressure on an arbitrary subset and measure-theoretic pressure of Borel probability measures for finitely generated semigroup actions. Let ( X , ) be a system, where X is a compact metric space and is a finite family of continuous maps on X . Given a continuous function f on X , we define Pesin-Pitskel topological pressure for any subset Z ⊂ X and measure-theoretical pressure for any , where denotes the set of all Borel probability measures on X . For any non-empty compact subset Z of X , we show that
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-021-0403-9