On the probability of positive finite-time Lyapunov exponents on strange non-chaotic attractors

TL;DR

This paper investigates the likelihood of positive finite-time Lyapunov exponents on strange non-chaotic attractors, showing that this probability diminishes exponentially with time, which has implications for early-warning signals in dynamical systems.

Contribution

It provides a rigorous proof that the probability of positive finite-time Lyapunov exponents decays exponentially on certain attractors, advancing understanding of finite-time stability in forced systems.

Findings

Probability of positive Lyapunov exponents decays exponentially with time

Finite-time Lyapunov exponents can serve as early-warning signals

Results apply to a class of quasiperiodically forced monotone maps

Abstract

We study strange non-chaotic attractors in a class of quasiperiodically forced monotone interval maps known as pinched skew products. We prove that the probability of positive time-N Lyapunov exponents, with respect to the unique physical measure on the attractor, decays exponentially as N goes to infinity. The motivation for this work comes from the study of finite-time Lyapunov exponents as possible early-warning signals of critical transitions in the context of forced dynamics.