A note on nonwandering set of a nonautonomous discrete dynamical system

Abstract

In this paper, we study nonwandering set and recurrent set for the non-autonomous discrete dynamical system given by a sequence {f n } ∞ n=0 of homeomorphisms on a compact metric space.

Various Non-autonomous Notions for Borel Measures

“…The set of such points is denoted by Ω(F ). (ii) F is said to be transitive with respect to µ ∈ M (X) if the set of transitive points (i.e; points x for which ω(F, x) = X) has positive measure with respect to µ. Lemma 5.9 [16] Let F = {f n } n∈N be a time varying bi-measurable map on a metric space (X, d). Then, Ω(F ) is a closed subset of X.…”