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

Abstract

This works investigates the Lyapunov-Oseledets spectrum of transfer operator cocycles associated to one-dimensional random paired tent maps depending on a parameter , quantifying the strength of the leakage between two nearly invariant regions. We show that the system exhibits metastability, and identify the second Lyapunov exponent λ 2 within an error of order 2 | log |. This approximation agrees with the naive prediction provided by a time-dependent two-state Markov chain. Furthermore, it is shown that λ 1 = 0 and λ 2 are simple, and the only exceptional Lyapunov exponents of magnitude greater than − log 2 + O(log log 1 / log 1 ).