Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2020; 35(1): 287-300

Printed January 31, 2020

https://doi.org/10.4134/CKMS.c180538

Copyright © The Korean Mathematical Society.

Topologically stable measures in non-autonomous systems

Pramod Das, Tarun Das

University of Delhi; University of Delhi

Abstract

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

Keywords: Expansive homeomorphisms, expansive measures, shadowing, persistence, topological stability

MSC numbers: Primary 54H20, Secondary 37B55