Robustly non-hyperbolic transitive endomorphisms on 𝕋²

He, Baolin; Gan, Shaobo

doi:10.1090/S0002-9939-2013-11527-3

Robustly non-hyperbolic transitive endomorphisms on $\mathbb {T}^2$
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by Baolin He and Shaobo Gan

Proc. Amer. Math. Soc. 141 (2013), 2453-2465

DOI: https://doi.org/10.1090/S0002-9939-2013-11527-3

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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