Historic Behaviour for Random Expanding Maps on the Circle

Abstract

Takens constructed a residual subset of the state space consisting of initial points with historic behaviour for expanding maps on the circle. We prove that this statistical property of expanding maps on the circle is preserved under small random perturbations. The proof is given by establishing a random Markov partition, which follows from a random version of Shub's Theorem on topological conjugacy with the folding maps.

References in corpus (2)

• Takens' last problem and existence of non-trivial wandering domains
• On Takens' Last Problem: tangencies and time averages near heteroclinic networks