Random minimality and continuity of invariant graphs in random dynamical systems

Abstract

We study dynamical systems forced by a combination of random and deterministic noise and provide criteria, in terms of Lyapunov exponents, for the existence of random attractors with continuous structure in the fibres. For this purpose, we provide suitable random versions of the semiuniform ergodic theorem and also introduce and discuss some basic concepts of random topological dynamics.

arXiv commentAs one of the three main results of the first version was partially known (Y. Cao, 2006), we reorganized the material and changed the title of the submission in order to emphasize the other results and some new concepts introduced in this paper. (15 pages)