Lyapunov exponents for transfer operator cocycles of metastable maps: a quarantine approach

2021/01/17 by González-Tokman, Cecilia, Quas, Anthony
#37H15 #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.2101.06588

Abstract

This works investigates the Lyapunov-Oseledets spectrum of transfer operator cocycles associated to one-dimensional random paired tent maps depending on a parameter ε, quantifying the strength of the leakage between two nearly invariant regions. We show that the system exhibits metastability, and identify the second Lyapunov exponent λ₂^ε within an error of order ε²|log ε|. This approximation agrees with the naive prediction provided by a time-dependent two-state Markov chain. Furthermore, it is shown that λ₁^ε=0 and λ₂^ε are simple, and are the only exceptional Lyapunov exponents of magnitude greater than -log2+ O(loglog\tfrac 1ε/log\tfrac 1ε).

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