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arXiv · 2101.06588

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

Cecilia González-Tokman·Anthony Quas
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Abstract

This works investigates the Lyapunov-Oseledets spectrum of transfer operator cocycles associated to one-dimensional random paired tent maps depending on a parameter $\epsilon$, quantifying the strength of the \emph{leakage} between two nearly invariant regions. We show that the system exhibits metastability, and identify the second Lyapunov exponent $\lambda_2^\epsilon$ within an error of order $\epsilon^2|\log \epsilon|$. This approximation agrees with the naive prediction provided by a time-dependent two-state Markov chain. Furthermore, it is shown that $\lambda_1^\epsilon=0$ and $\lambda_2^\epsilon$ are simple, and are the only exceptional Lyapunov exponents of magnitude greater than $-\log2+ O(\log\log\tfrac 1\epsilon/\log\tfrac 1\epsilon)$.

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Cecilia González-Tokman, Anthony Quas. 2021-01-17. Lyapunov exponents for transfer operator cocycles of metastable maps: a quarantine approach. https://arxiv.org/abs/2101.06588

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