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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Entropy points and applications


Authors: Xiangdong Ye and Guohua Zhang
Journal: Trans. Amer. Math. Soc. 359 (2007), 6167-6186
MSC (2000): Primary 37A05, 37A35
Published electronically: July 23, 2007
MathSciNet review: 2336322
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Abstract | References | Similar Articles | Additional Information

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.


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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
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

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04357-7
PII: S 0002-9947(07)04357-7
Keywords: Topological entropy, entropy for a measure, entropy tuple, entropy point
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)
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.