Perturbation theory for Lyapunov exponents of a toral map: extension of a result of Shub and Wilkinson

2001/07/11 by David Ruelle, Ruelle, David
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #nlin.CD

paper · pdf · doi:10.48550/arxiv.nlin/0107022

15 pages, this new version has a few confusing misprints corrected

openalex publication_date 2001/07/11 · arxiv created 2001/07/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Starting from a hyperbolic toral automorphism, we obtain, for a small volume preserving perturbation, an exact and rigorous second order perturbation expansion of the Lyapunov exponents.

Related

• Some results on perturbations to Lyapunov exponents
• Analiticity of the Lyapunov exponents of perturbed toral automorphisms
• Local rigidity of Lyapunov spectrum for toral automorphisms
• Lyapunov exponents in complex dynamics and potential theory
• Lyapunov exponents of hyperbolic measures and hyperbolic periodic orbits