Approximation property on entropies for surface diffeomorphisms
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- by Wanlou Wu and Jiansong Liu PDF
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Abstract:
In this paper, we prove that for any $C^1$ surface diffeomorphism $f$ with positive topological entropy, there exists a diffeomorphism $g$ arbitrarily close (in the $C^1$ topology) to $f$ exhibiting a horseshoe $\Lambda$, such that the topological entropy of $g$ restricted on $\Lambda$ can arbitrarily approximate the topological entropy of $f$. This extends a classical result of Katok for $C^{1+\alpha }(\alpha >0)$ surface diffeomorphisms.References
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Additional Information
- Wanlou Wu
- Affiliation: School of Mathematical Sciences, Soochow University, Suzhou, 215006, People’s Republic of China
- MR Author ID: 1306800
- Email: wuwanlou@163.com, wanlouwu1989@gmail.com
- Jiansong Liu
- Affiliation: School of Mathematical Sciences, Soochow University, Suzhou, 215006, People’s Republic of China
- Email: jsliu1205@163.com, jsliu@stu.suda.edu.cn
- Received by editor(s): March 19, 2018
- Received by editor(s) in revised form: February 22, 2019, April 3, 2019, and April 9, 2019
- Published electronically: July 9, 2019
- Communicated by: Wenxian Shen
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 223-233
- MSC (2010): Primary 37A35, 37B10, 37C25, 37D05, 37E30
- DOI: https://doi.org/10.1090/proc/14670
- MathSciNet review: 4042845