Analiticity of the Lyapunov exponents of perturbed toral automorphisms
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915023499034624 |
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| author | Marin, Gian Marco Bonetto, Federico Corsi, Livia |
| author_facet | Marin, Gian Marco Bonetto, Federico Corsi, Livia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04957 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Analiticity of the Lyapunov exponents of perturbed toral automorphisms Marin, Gian Marco Bonetto, Federico Corsi, Livia Dynamical Systems 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. |
| title | Analiticity of the Lyapunov exponents of perturbed toral automorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2308.04957 |