子集上的拓扑压的变分原理.pdfVIP

子集上的拓扑压的变分原理 中文摘要 中 文 摘 要 本文研究了任意子集上的Pesin-Pitskel拓扑压与关于Borel概率测度的测度压之间 的关系，将丰德军和黄文教授最近的关于拓扑熇的工作丨27]推广到了拓扑压上. 具体来说, 本文定义了关于Borel概率测度的测度压PM(r ，/),证明了 Pb(T ，/ ，K) = sup{P^(T, f ) : H € M (X ),fx(K) = I } , 其 中 M ( X) 表 示 上所有 Borel概率测度组成的集合，K C 是非空紧子集，PS(T, f , K ) 是集合 K 上的 Pesin-Pitskel拓扑压.进一步，如果 Z X 是一个解析集 ，则 PB(T ，f ，Z) = sup {PB(T ，f ，K) : K C Z , K 是紧集} • 另外，本文还证 明了 Pesin-Pitskel拓扑压是由测度压所决定的. 关键词：测度压；变分原理；Borel概率测度；拓扑压. 作 者：汤信佳 指导老师：赵云 英文摘要 子集上的拓扑压的变分原理 Variational Principle for Topological Pressures on Subsets Abstract This paper studies the relations between Pesin-Pitskel topological pressure on an arbitrary subset and measure theoretic pressure of Borel probability measures, which extends Feng and Huang’s recent result on entropies [27] for pressures. More precisely, this paper defines the measure theoretic pressure Pm(T, /) for any Borel probability measure, and shows that PB(T ，f ，K) = s u p { (r ，/) : // G M (X ), = l} ? where M (X ) is the space of all Borel probability measures, K C X is Si non-empty compact subset and Pb(T^ /, K) is the Pesin-Pitskel topological pressure on K . Furthermore, \i Z C X is an analytic subset, then Pb(T, /, Z) = sup{PB(r, /, K) : K C Z is compact}. And this paper also shows that Pesin-Pitskel topological pressure can be determined by the measure theoretic pressure of measures. Keywords: measure-theoretic pressure, variational principle, Borel probability measure, topological pressure.