Robustly non-hyperbolic transitive endomorphisms on $\mathbb {T}^2$
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Abstract:
We prove that for any regular endomorphism $f$ on a 2-torus $\mathbb {T}^2$ which is not one to one, there is a regular map $g$ homotopic to $f$ such that $g$ is $C^1$ robustly non-hyperbolic transitive. We also introduce interesting blender phenomena (a fat horseshoe) of 2-dimensional endomorphisms, which play an important role in our construction of some examples.References
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Additional Information
- Baolin He
- Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- Email: hebaolin@pku.edu.cn
- Shaobo Gan
- Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- Email: gansb@math.pku.edu.cn
- Received by editor(s): August 25, 2011
- Received by editor(s) in revised form: October 23, 2011
- Published electronically: April 5, 2013
- Additional Notes: This work is supported by 973 program 2011CB808002 and NSFC 11025101
- Communicated by: Yingfei Yi
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2453-2465
- MSC (2010): Primary 37D30
- DOI: https://doi.org/10.1090/S0002-9939-2013-11527-3
- MathSciNet review: 3043026