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arXiv · 2006.00406

Lyapunov exponents everywhere and rigidity

Fernando Micena·Rafael de la Llave
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Abstract

In the present work we obtain rigidity results analysing the set of regular points, in the sense of Oseledec's Theorem. It is presented a study on the possibility of an Anosov diffeomorphisms having all Lyapunov exponents defined everywhere. We prove that this condition implies local rigidity of an Anosov automorphism of the torus $\mathbb{T}^d, d \geq 3,$ $C^1-$close to a linear automorphism diagonalizable over $\mathbb{R}$ and such that its characteristic polynomial is irreducible over $\mathbb{Q}.$

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Fernando Micena, Rafael de la Llave. 2020-05-31. Lyapunov exponents everywhere and rigidity. https://arxiv.org/abs/2006.00406

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