Analiticity of the Lyapunov exponents of perturbed toral automorphisms

2023/08/09 by Gian Marco Marin, Marin, Gian Marco, Federico Bonetto +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2308.04957

openalex publication_date 2023/08/09 · openalex created_date 2023/08/11 · openalex updated_date 2026/07/28

Abstract

We consider a dynamical system generated by an analytic perturbation A_ε of an analytic Anosov diffeomorphism A₀ of \TTT^d. We show that, if A₀ 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 dA₀ 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.

Related

• Perturbation theory for Lyapunov exponents of a toral map: extension of a result of Shub and Wilkinson
• Lyapunov exponents everywhere and rigidity
• Local rigidity of Lyapunov spectrum for toral automorphisms
• Flexibility of Lyapunov exponents with respect to two classes of\n measures on the torus
• Lyapunov exponents and rigidity of Anosov automorphisms and skew products