Variational Principle for Topological Pressure on Subsets of Free Semigroup Actions
| Autor: | Xing Fu Zhong, Zhi Jing Chen |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Acta Mathematica Sinica, English Series. 37:1401-1414 |
| ISSN: | 1439-7617 1439-8516 |
| DOI: | 10.1007/s10114-021-0403-9 |
| Popis: | 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, $${\cal G}$$ ) be a system, where X is a compact metric space and $${\cal G}$$ is a finite family of continuous maps on X. Given a continuous function f on X, we define Pesin-Pitskel topological pressure $${P_{\cal G}}(Z,f)$$ for any subset Z ⊂ X and measure-theoretical pressure $${P_{\mu ,{\cal G}}}(X,f)$$ for any $$\mu \in {\cal M}(X)$$ , where $${\cal M}(X)$$ denotes the set of all Borel probability measures on X. For any non-empty compact subset Z of X, we show that $${P_{\cal G}}(Z,f) = \sup \{ {P_{\mu ,{\cal G}}}(X,f):\mu \in {\cal M}(X),\mu (Z) = 1\} .$$ |
| Databáze: | OpenAIRE |
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