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arXiv · 2006.00407

Rigidity for Some Cases of Anosov Endomorphisms of Torus

Fernando Micena
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Abstract

We obtain smooth conjugacy between non-necessarily special Anosov endomorphisms in the conservative case. Among other results, we prove that a strongly special $C^{\infty}-$Anosov endomorphism of $\mathbb{T}^2$ and its linearization are smoothly conjugated since they have the same periodic data. Assuming that for a strongly special $C^{\infty}-$Anosov endomorphism of $\mathbb{T}^2$ every point is regular (in Oseledec's Theorem sense), then we obtain again smooth conjugacy with its linearization. We also obtain some results on local rigidity of linear Anosov endomorphisms of $d-$torus, where $d \geq 3,$ under periodic data assumption. The study of differential equations defined on invariant leaves plays an important role in rigidity problems such as those treated here.

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Fernando Micena. 2022-09-13. Rigidity for Some Cases of Anosov Endomorphisms of Torus. https://arxiv.org/abs/2006.00407

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