Entropy points and applications
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- by Xiangdong Ye and Guohua Zhang PDF
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Abstract:
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.References
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Additional Information
- Xiangdong Ye
- Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
- MR Author ID: 266004
- Email: yexd@ustc.edu.cn
- Guohua Zhang
- Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
- Email: ghzhang@mail.ustc.edu.cn
- Received by editor(s): September 15, 2005
- Received by editor(s) in revised form: May 15, 2006
- Published electronically: July 23, 2007
- Additional Notes: Both authors were partially supported by Ministry of Education (no. 0358053), and the first author was partially supported by NSFC (no. 10531010)
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 6167-6186
- MSC (2000): Primary 37A05, 37A35
- DOI: https://doi.org/10.1090/S0002-9947-07-04357-7
- MathSciNet review: 2336322