Random product of quasi-periodic cocycles

2019/07/01 by Bezerra, Jamerson, Poletti, Mauricio · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.00815

Abstract

Given a finite set of quasi-periodic cocycles the random product of them is defined as the random composition according to some probability measure. We prove that the set of C^r, 0≤ r ≤ ∞ (or analytic) k+1-tuples of quasi periodic cocycles taking values in SL₂(ℝ) such that the random product of them has positive Lyapunov exponent contains a C⁰ open and C^r dense subset which is formed by C⁰ continuity point of the Lyapunov exponent For k+1-tuples of quasi periodic cocycles taking values in GL_d(ℝ) for d>2, we prove that if one of them is diagonal, then there exists a C^r dense set of such k+1-tuples which has simples Lyapunov spectrum and are C⁰ continuity point of the Lyapunov exponent.

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• Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms

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