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
DOI: 10.12677/PM.2021.112031, PDF,    国家自然科学基金支持
作者: 郑伊楠, 肖 倩：华南理工大学数学学院，广东 广州
关键词: 拓扑r压；拓扑压；斜积变换；自由半群作用；Topological r-Pressure； Topological Pressure； Skew-Product Transformations； Free Semigroup Actions
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。
Abstract: 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.
文章引用：郑伊楠, 肖倩. 自由半群作用的拓扑r压和拓扑压[J]. 理论数学, 2021, 11(2): 222-236. https://doi.org/10.12677/PM.2021.112031

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