Random semi-horseshoe for partially hyperbolic systems driven by an external force

Abstract

In this paper, we consider the symbolic representation of systems driven by an invertible measurable mapping on a measurable space. We prove that when such a system possesses an equicontinuous uniformly expanding subbundle, then it has a subsystem of its iterations randomly semi-conjugating to the full shift on two symbols. Examples such as random perturbation of partially hyperbolic systems, random composition of partially hyperbolic automorphisms on 3-d tori with a fixed central direction, and fiber partially hyperbolic maps on 3-d tori without stable subbundles are under consideration.