Continuity of Lyapunov Exponents for Random 2D Matrices

2010/12/04 by Carlos Bocker, Carlos Bocker-Neto, Marcelo Viana +2
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.1012.0872

arxiv created 2010/12/04 · openalex publication_date 2010/12/04 · arxiv updated 2010/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Lyapunov exponents of locally constant GL(2;C)-cocycles over Bernoulli shifts depend continuously on the cocycle and on the invariant probability. The Oseledets decomposition also depends continuously on the cocycle, in measure.

Citations

• Extremal Lyapunov exponents: an invariance principle and applications
• Products of Random Matrices
• Random matrix products and measures on projective spaces

Related

• Lyapunov Exponents of Linear Cocycles Over Markov Shifts
• Large deviation type estimates for random cocycles
• An abstract continuity theorem of the Lyapunov exponents
• Random 2D linear cocycles II: statistical properties
• Random 2D linear cocycles I: dichotomic behavior