Horseshoes and Lyapunov exponents for Banach cocycles over nonuniformly hyperbolic systems

2019/02/15 by Rui Zou, Zou, Rui, Yongluo Cao +1 · 1 citation
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1902.05768

openalex publication_date 2019/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a C^r(r>1) diffeomorphism of a compact Riemannian manifold M, preserving an ergodic hyperbolic measure μ with positive entropy, and let A be a Hölder continuous cocycle of injective bounded linear operators acting on a Banach space X. We prove that there is a sequence of horseshoes for f and dominated splittings for A on the horseshoes, such that not only the measure theoretic entropy of f but also the Lyapunov exponents of A with respect to μ can be approximated by the topological entropy of f and the Lyapunov exponents of A on the horseshoes, respectively.

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• Stable manifolds, Horseshoes and Lyapunov exponents for C¹ diffeomorphisms without domination

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