RECURRENCE IN SYSTEMS WITH RANDOM PERTURBATIONS

We introduce the notion of (f, δ)-recurrence for the so-called (f, δ)-processes. We show that if a function of type 2^∞ has no attractive periodic points of periods greater than 2^N for some positive integer N and has an infinite ω-limit set, then each point belonging to its infinite ω-limit set is (f, δ)-recurrent provided that δ is small enough.