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

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arxiv 2111.00683 v1 pith:X6WGGEDE submitted 2021-11-01 math.DS

Jamerson Bezerra , Adriana Sánchez , El Hadji Yaya Tall This is my paper · ORCID
classification math.DS
keywords lyapunovexponentsanalyticallycocycleslambdaquasi-periodicrandomreal
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abstract

We show that the top Lyapunov exponent $\lambda_+(p)$ , $p = (p_1, \cdots, p_N)$ 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 $\lambda_+(p)$ is simple. Moreover if the spectrum at $p$ is simple (all Lyapunov exponents having multiplicity one ) then all Lyapunov exponents depend real analytically on $p$.

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  1. Analyticity of Lyapunov Exponents for Mixed Markov Quasi-Periodic Cocycles

    math.DS 2026-08 conditional novelty 6.0 of 10

    The top Lyapunov exponent of a primitive Markov quasi-periodic cocycle with simple top spectrum has a holomorphic extension in a complex neighborhood of the transition matrix.

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