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arXiv · 1506.06945

A Garden of Eden theorem for Anosov diffeomorphisms on tori

Tullio Ceccherini-Silberstein·Michel Coornaert
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Abstract

Let $f$ be an Anosov diffeomorphism of the $n$-dimensional torus ${\mathbb{T}}^n$ and $\tau$ a continuous self-mapping of ${\mathbb{T}}^n$ commuting with $f$. We prove that $\tau$ is surjective if and only if the restriction of $\tau$ to each homoclinicity class of $f$ is injective.

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Tullio Ceccherini-Silberstein, Michel Coornaert. 2015-06-23. A Garden of Eden theorem for Anosov diffeomorphisms on tori. https://arxiv.org/abs/1506.06945

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