Random minimality and continuity of invariant graphs in random dynamical   systems
  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. 
Tobias J\"ager and Gerhard Keller
math.DS