Entropy points and applications

By Xiangdong Ye, Guohua Zhang. 2007

65 citations recorded by the source corpus.

First notions of entropy point and uniform entropy point are introduced using Bowen's definition of topological entropy. Some basic properties of the notions are discussed. As an application it is shown that for any topological dynamical system there is a countable closed subset whose Bowen entropy is equal to the entropy of the original system. Then notions of C-entropy point are introduced along the line of entropy tuple both in topological and measure-theoretical settings. It is shown that each C-entropy point is an entropy point, and the set of C-entropy points is the union of sets of C-entropy points for all invariant measures.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/83bc24a51d577a6b9b31e3656552a5fd54ebb611

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In Mathematical Physics

1. Xiangdong Ye
2. Guohua Zhang
3. Wen Huang
4. A. Dooley
5. Eli Glasner
6. Jian Li
7. Felipe Garc'ia-Ramos
8. Hanfeng Li

Citations in the corpus

• Combinatorial lemmas and applications to dynamics (2009, background): “ing entropy points and entropy sets see [35,8,6], and for a survey see [12]).”
• Local Entropy Theory of a Random Dynamical System (2011, background): “v systems [3, 4]. Stimulated by these two papers, local entropy theory for continuous actions of a countable amenable group on compact metric spaces developed rapidly during the last two decades, see [5, 6, 7, 21, 29, 32, 34, 35, 36, 37, 38, 64, 72]. It has been studied for countable sofic group acti”
• Local entropy theory for a countable discrete amenable group action (2010, background): “From then on, the local entropy theory of Z -actions have been made great achievements [1, 2, 3, 4, 5, 11, 16, 21, 23, 24, 25, 27, 40, 46], see also the relevant chapters in [17] and the survey papers [19, 20].”