Topological pressures for $\epsilon$-stable and stable sets
Topological pressures for $\epsilon$-stable and stable sets
复制标题
DOI：
10.2140/pjm.2013.263.117
复制
发表时间：
2010-08
期刊：
影响因子：
--
通讯作者：
Xianfeng Ma;Ercai Chen
中科院分区：
文献类型：
--
作者：
Xianfeng Ma;Ercai Chen
研究了正熵系统中稳定集的原像和稳定集的某些闭子集的拓扑压力。证明了任何拓扑系统的拓扑压都可以用稳定集的原像的拓扑压来计算。对于正熵拓扑系统的测度论“相当大”集合中任一点的稳定集或不稳定集的构造闭子集，特别是对于稳定集和不稳定集的闭包中包含的弱混合子集，证明了这些子集的拓扑压力不小于测度论压力.
Topological pressures of the preimages of $\epsilon$-stable sets and some certain closed subsets of stable sets in positive entropy systems are investigated. It is showed that the topological pressure of any topological system can be calculated in terms of the topological pressure of the preimages of $\epsilon$-stable sets. For the constructed closed subset of the stable set or the unstable set of any point in a measure-theoretic `rather big' set of a topological system with positive entropy, especially for the weakly mixing subset contained in the closure of stable set and unstable set, it is proved that topological pressures of these subsets can be no less than the measure-theoretic pressure.