Analyticity of the Lyapunov exponents of random products of quasi-periodic cocycles

2021/11/01 by Jamerson Bezerra, Adriana Sánchez, Bezerra, Jamerson +3
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2111.00683

Abstract

We show that the top Lyapunov exponent λ₊(p) , p = (p₁, ⋯, p_N) with p_i >0 for each i, associated with a random product of quasi-periodic cocycles depends real analytically on the transition probabilities p whenever λ₊(p) is simple. Moreover if the spectrum at p is simple (all Lyapunov exponents having multiplicity one ) then all Lyapunov exponents depend real analytically on p.

Related

• Random product of quasi-periodic cocycles
• Continuity, positivity and simplicity of the Lyapunov exponents for quasi-periodic cocycles
• Hölder continuity of Lyapunov exponents for non-invertible and non-compact random cocycles
• Lyapunov exponents with multiplicity 1 for deterministic products of matrices
• Continuity of the Lyapunov exponent for analytic multi-frequency quasiperiodic cocycles