Weighted Topological Entropy of the Set of Generic Points in Topological Dynamical Systems
Weighted Topological Entropy of the Set of Generic Points in Topological Dynamical Systems
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DOI：
10.1007/s10884-017-9575-5
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发表时间：
2018-09
影响因子：
1.3
通讯作者：
Cao Zhao;Ercai Chen;Xiaoyao Zhou;Zheng Yin
中科院分区：
文献类型：
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作者：
Cao Zhao;Ercai Chen;Xiaoyao Zhou;Zheng Yin
本文研究了动力系统中遍历测度的一般点的加权拓扑熵。本文证明了遍历测度的一般点的加权拓扑熵等于其加权测度熵，推广了Bowen（Trans Am Math Soc 184：125-136，1973）的经典结果。作为应用，我们还研究了高维环面上一类斜积扩张映射的通有点的维数。
This article is devoted to the investigation of the weighted topological entropy of generic points of the ergodic measures in dynamical systems. We showed that the weighted topological entropy of generic points of the ergodic measureis equal to the weighted measure entropy ofwhich generalized the classical result of Bowen (Trans Am Math Soc 184:125–136, 1973). As an application, we also use the result to study the dimension of generic points for a class of skew product expanding maps on high dimensional tori.