Strictly ordered minimal subsets of a class of convex monotone skew-product semiflows

Abstract

We study the topological and ergodic structure of a class of convex and monotone skew-product semiflows. We assume the existence of two strongly ordered minimal subsets K 1, K 2 and we obtain an ergodic representation of their upper Lyapunov exponents. In the case of null upper Lyapunov exponents, we obtain a lamination into minimal subsets of an intermediate region where the restriction of the semiflow is affine. In the hyperbolic case, we deduce the long-time behaviour of every trajectory ordered with K 2. Some examples of skew-product semiflows generated by non-autonomous differential equations and satisfying the assumptions of monotonicity and convexity are also presented.