拓扑近压的一点注记  

A note on the topological nearly pressure

作　　者：张俊杰 赵操 ZHANG Junjie;ZHAO Cao(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《安徽大学学报（自然科学版）》2024年第3期33-38,共6页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11901419);江苏省研究生科研创新计划(KYCX23_3300);上海市教委“晨光计划”项目(20CGB09)。

摘　　要：拓扑压是动力系统热力学公式的主要内容之一,是拓扑熵的推广.引入了拓扑近压的概念并研究了其相关基本性质,即对R-映射的动力系统,给出了近紧子集的拓扑近压的定义.此外,在非紧集合上定义了Pesin正则拓扑压并给出相关基本性质.最后,证明了拓扑R动力系统中二者的等价性.Topological pressure is one of the main contents of the thermodynamic formula of dynamical systems,and it is the generalization of topological entropy.This paper introduced the concept of topological nearly pressure and studied its basic properties.Specifically,we gave the definition of topological nearly pressure of the nearly compact subsets about the R-mapped dynamical system.In addition,for non-compact sets,the Pesin regular topological pressure was defined and related basic properties were given.Finally,the equivalence of the two definitions was proved for topological R dynamical systems.

关 键 词：拓扑近压 拓扑熵 拓扑R动力系统 

分 类 号：O156[理学—数学]