Positive Lyapunov exponents for symplectic cocycles

2014/07/01 by Mário Bessa, Bessa, Mario, Paulo Varandas +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1407.0336

openalex publication_date 2014/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we give a positive answer to a question posed by Viana on the existence of positive Lyapunov exponents for symplectic cocycles. Actually, we prove that for an open and dense set of Holder symplectic cocycles over a non-uniformly hyperbolic diffeomorphism there are non-zero Lyapunov exponents with respect to any invariant ergodic measure with the local product structure.

Citations

• Lyapunov exponents with multiplicity 1 for deterministic products of matrices
• Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents

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