Non-uniform hyperbolicity of maps on $\mathbb{T}^2$

Sebastián Ramírez; Kendry J. Vivas

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arXiv · 2312.16742

Non-uniform hyperbolicity of maps on $\mathbb{T}^2$

Sebastián Ramírez·Kendry J. Vivas

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Abstract

In this paper we prove that the homotopy class of non-homothety linear endomorphisms on $\mathbb{T}^2$ with determinant greater than 2 contains a $C^1$ open set of non-uniformly hyperbolic endomorphisms. Furthermore, we prove that the homotopy class of non-hyperbolic elements (having either $1$ or $-1$ as an eigenvalue) whose degree is large enough contains non-uniformly hyperbolic endomorphisms that are also $C^2$ stably ergodic. These results provide partial answers to certain questions posed in arXiv:2206.08295v2

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BibTeX RIS

Sebastián Ramírez, Kendry J. Vivas. 2023-12-27. Non-uniform hyperbolicity of maps on $\mathbb{T}^2$. https://arxiv.org/abs/2312.16742

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