Entropy dimension of measure preserving systems
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- by Dou Dou, Wen Huang and Kyewon Koh Park PDF
- Trans. Amer. Math. Soc. 371 (2019), 7029-7065 Request permission
Abstract:
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This combinatorial approach provides us with a new insight for analyzing entropy zero systems. We also define the dimension set of a system to investigate the structure of the randomness of the factors of a system. The notion of a uniform dimension in the class of entropy zero systems is introduced as a generalization of a K-system in the case of positive entropy. We investigate joinings among entropy zero systems and prove the disjointness property among some classes of entropy zero systems using dimension sets. Given a topological system, we compare topological entropy dimension with metric entropy dimension.References
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Additional Information
- Dou Dou
- Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiangsu, 210093, People’s Republic of China
- MR Author ID: 713740
- Email: doumath@163.com
- Wen Huang
- Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
- MR Author ID: 677726
- Email: wenh@mail.ustc.edu.cn
- Kyewon Koh Park
- Affiliation: Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul 130-722, Korea
- MR Author ID: 136240
- Email: kkpark@kias.re.kr
- Received by editor(s): May 5, 2017
- Received by editor(s) in revised form: January 9, 2018, and February 13, 2018
- Published electronically: September 24, 2018
- Additional Notes: The first author is supported by NNSF of China (Grant Nos. 10901080, 11271191, 11790274).
The second author is supported by NNSF of China (Grant Nos. 11225105 and 11431012).
The third author is supported in part by NRF 2010-0020946. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 7029-7065
- MSC (2010): Primary 37A35, 37A05, 28D20
- DOI: https://doi.org/10.1090/tran/7542
- MathSciNet review: 3939569