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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Robustly non-hyperbolic transitive endomorphisms on $ \mathbb{T}^2$


Authors: Baolin He and Shaobo Gan
Journal: Proc. Amer. Math. Soc. 141 (2013), 2453-2465
MSC (2010): Primary 37D30
Published electronically: April 5, 2013
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11527-3
PII: S 0002-9939(2013)11527-3
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.