一类非紧集的拓扑压的变分原理  

The Variational Principle of Topological Pressure on Certain Non-compact Subset

作　　者：王威 WANG Wei(Basic Department of JinShen College,Nanjing Audit University,Nanjing Jiangsu 210023,China)

机构地区：[1]南京审计大学金审学院基础部,南京210023

出　　处：《西华师范大学学报（自然科学版）》2018年第4期413-419,共7页Journal of China West Normal University(Natural Sciences)

摘　　要：对动力系统中经典的紧致集合上的遍分原理研究是一个热门方向,现推广至非紧致集合EF(α)={x∈X∶λF(x)=α}上,并定义了在该集合下的拓扑压。论文主要工作给出该非紧集合上的拓扑压的变分原理并进行论证,在证明过程中利用了一系列的引理来帮助完成定理的证明,其中非紧集中的F={fn}∞n=1是指(X,T)上的极限次可加连续函数列。论文在最后给出关于BS-维数的应用和两个其它应用。Variational principle of the classical compact set in dynamic system is a hot research direction.It is popularized to non-compact subset EF(α)={x∈X∶λF(x)=α}and defines topological pressure under the set.The main work of this paper is to give the variational principle of topological pressure on non compact set and demonstrate that a series of lemmas are used in the process of proof.Among which,F={fn}∞n=1 is a limit sub-additive family of continuous function defined on(X,T).At the end of the paper,the application of BS-dimension and two other applications are given.

关 键 词：极限次可加连续函数列 非紧集合的拓扑压 变分原理 LYAPUNOV指数 熵 

分 类 号：O189[理学—数学]