自由半群作用的拓扑r压和拓扑压  

Topological r-Pressure and Topological Pressure of Free Semigroup Actions

作　　者：郑伊楠 肖倩 

机构地区：[1]华南理工大学数学学院,广东 广州

出　　处：《理论数学》2021年第2期222-236,共15页Pure Mathematics

摘　　要：本文给出了紧致度量空间上自由半群作用的拓扑r压的定义,并给出了它的一些性质。通过斜积变换为介质,我们可以得到以下两个主要结果。1) 将拓扑r压的极限推广到自由半群作用(r→0)。2) 假设fi,i=0,1,…,m-1是紧致度量空间上的同胚,则对于任意连续函数,我们证明了f0,…,fm-1的拓扑压等于f0-1,…,fm-1-1的拓扑压。In this paper, we introduce the definition of topological r-pressure of free semigroup actions on compact metric space and provide some properties of it. Through skew-product transformation into a medium, we can obtain the following two main results. 1) We extend the result that the top-ological pressure is the limit of topological r-pressure to free semigroup actions (r→0). 2) Let fi,i=0,1,…,m-1, be homeomorphisms on a compact metric space. For any continuous function, we verify that the topological pressure of f0,…,fm-1 equals the topological pressure of f0-1,…,fm-1-1.

关 键 词：拓扑r压 拓扑压 斜积变换 自由半群作用 

分 类 号：O17[理学—数学]