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arXiv · 2308.04957

Analiticity of the Lyapunov exponents of perturbed toral automorphisms

Gian Marco Marin·Federico Bonetto·Livia Corsi
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Abstract

We consider a dynamical system generated by an analytic perturbation $A_\varepsilon$ of an analytic Anosov diffeomorphism $A_0$ of $\TTT^d$. We show that, if $A_0$ admit a splitting of $\mathrm T\mathds T^d$ in $k$ invariant subspaces, there exists a {\it partial conjugation} $\mathcal H_\e$ of $dA_\e$ and $dA_0$ that preserves the splitting and is analytic in $\e$. This show that the splitting can be extended to $A_\e$. As an application of this results, we obtain that the Lyapunov exponents, if non degenerate, are analytic functions of the perturbation.

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Gian Marco Marin, Federico Bonetto, Livia Corsi. 2023-08-09. Analiticity of the Lyapunov exponents of perturbed toral automorphisms. https://arxiv.org/abs/2308.04957

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