Universal gap growth for Lyapunov exponents of perturbed matrix products
Abstract: In this talk, we address the question of quantitative simplicity of the Lyapunov spectrum of bounded matrix cocycles subjected to additive random perturbations. In dimensions 2 and 3, we show explicit lower bounds on the gaps between consecutive Lyapunov exponents of the perturbed cocycle, depending only on the scale of the perturbation. In arbitrary dimensions, we establish existence of a universal lower bound on these gaps. A novelty of this work is that the bounds provided are uniform over all choices of the original sequence of matrices, making no stationarity assumptions. Hence, our results apply to random and sequential dynamical systems alike. (Joint work with Jason Atnip, Gary Froyland and Anthony Quas.)