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arXiv · 2305.02298

On Lyapunov exponents properties of special Anosov endomorphisms on $\mathbb{T}^d$

José Santana Costa·Fernando Micena
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Abstract

This work is addressed to study Anosov endomorphisms of $\mathbb{T}^d,$ $d\geq 3.$ We are interested to obtain metric and topological information on such Anosov endomorphism by comparison between their Lyapunov exponents and the ones of its linearization. We can characterize when a weak unstable foliation of a special Anosov endomorphism near to linear is an absolutely continuous foliation. Also, we show that in dimension $d \geq 3,$ it is possible to find a smooth special Anosov endomorphism being conservative but not Lipschitz conjugate with its linearization, in contrast with the smooth rigidity in dimension two.

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José Santana Costa, Fernando Micena. 2023-05-03. On Lyapunov exponents properties of special Anosov endomorphisms on $\mathbb{T}^d$. https://arxiv.org/abs/2305.02298

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