Preimage Entropy Dimension of Topological Dynamical Systems
Preimage Entropy Dimension of Topological Dynamical Systems
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DOI：
10.11650/tjm/210704
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发表时间：
2014-04
影响因子：
0.4
通讯作者：
Lei Liu;Xiaomin Zhou;Xiaoyao Zhou
中科院分区：
文献类型：
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作者：
Lei Liu;Xiaomin Zhou;Xiaoyao Zhou
给出了紧度量空间上连续映射原像熵维数的一个新定义，研究了原像熵维数的基本性质，并将原像熵维数与拓扑熵维数进行了比较.所定义的原像熵维具有拓扑熵维的各种基本性质，如子系统的原像熵维与原系统的原像熵维有界，拓扑共轭系统的原像熵维相同等.讨论了原像熵维数与原像熵之间的关系。
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated systems have the same preimage entropy dimension. Also, we discuss the relation between the preimage entropy dimension and the preimage entropy.