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

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\to \infty $. 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.