An entropy formula over the dynamical balls and its applications
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Abstract:
The Bowen topological entropy was introduced by Bowen in way which resembles the Hausdorff dimension. It is well-known that the Bowen topological entropy and the topological entropy of subsets are not equal in general. We show in the paper that the supremum of the Bowen topological entropy of the dynamical balls is the same as that of the topological entropy of the dynamical balls, which naturally implies that every positively countably expansive map is also positively entropy expansive. This answers a question posed by Artigue, Carvalho, Cordeiro, and Vieitez [Proc. Amer. Math. Soc. 150 (2022), pp. 3369–3378]. Besides, our main result is applied to find some other interesting phenomena.References
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Additional Information
- Tao Wang
- Affiliation: LCSM (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, People’s Republic of China
- Email: twang@hunnu.edu.cn
- Received by editor(s): January 7, 2021
- Received by editor(s) in revised form: June 25, 2021
- Published electronically: July 29, 2022
- Additional Notes: This work was partly supported by National Nature Science Foundation of China (12001192)
- Communicated by: Wenxian Shen
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 4743-4755
- MSC (2020): Primary 37B40, 37A35
- DOI: https://doi.org/10.1090/proc/15756