Variational Principle for Topological Pressure on Subsets of Free Semigroup Actions

• 作者: Xing Fu ZHONG Zhi Jing CHEN
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（9）
• 页码范围: 1401-1414
• 页数: 14页
• 语种: 英文

摘要

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,g) be a system,where X is a compact metric space and g is a finite family of continuous maps on X.Given a continuous function f on X,we define Pesin-Pitskel topological pressure Pg (Z,f)for any subset Z (∈) X and measure-theoretical pressure Pμ,g(X,f) for any μ ∈ M(X),where M(X)denotes the set of all Borel probability measures on X.For any non-empty compact subset Z of X,we show that Pg(Z,f) =sup{Pμ,g(X,f) :μ ∈ A(X),μ(Z) =1}.