Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases

2016/11/30 by Mário Bessa, Bessa, Mario, Jairo Bochi +9
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.1611.10158

openalex publication_date 2016/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A theorem of Viana says that almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents. In this note we extend this result to cocycles on any noncompact classical semisimple Lie group.

Citations

• Extremal Lyapunov exponents: an invariance principle and applications
• 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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