Various Non-autonomous Notions for Borel Measures

Abstract

We introduce and investigate the notions of expansiveness, topological stability and persistence for Borel measures with respect to time varying bi-measurable maps on metric spaces. We prove that expansive persistent measures are topologically stable in the class of all time varying homeomorphisms.

Generalizations of expansiveness in Non-Autonomous Discrete Systems

“…Roughly speaking, in an expansive dynamical system, every orbit can be accompanied by only one orbit with some certain constant. Expansive dynamical systems involve a large class of chaotic systems and in the last few decades an extensive study has been carried out on this property and its variants in both autonomous and non-autonomous systems [12,1,20,21,7]. One among these variants is the concept of n-expansiveness [15] which weakens the restriction on every orbit thus allowing at most n companion orbits with a certain constant.…”