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arXiv · 1808.06249

Local rigidity of Lyapunov spectrum for toral automorphisms

Andrey Gogolev·Boris Kalinin·Victoria Sadovskaya
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Abstract

We study the regularity of the conjugacy between an Anosov automorphism $L$ of a torus and its small perturbation. We assume that $L$ has no more than two eigenvalues of the same modulus and that $L^4$ is irreducible over $\mathbb Q$. We consider a volume-preserving $C^1$-small perturbation $f$ of $L$. We show that if Lyapunov exponents of $f$ with respect to the volume are the same as Lyapunov exponents of $L$, then $f$ is $C^{1+\text{H\"older}}$ conjugate to $L$. Further, we establish a similar result for irreducible partially hyperbolic automorphisms with two-dimensional center bundle.

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Andrey Gogolev, Boris Kalinin, Victoria Sadovskaya. 2018-08-19. Local rigidity of Lyapunov spectrum for toral automorphisms. https://arxiv.org/abs/1808.06249

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