Various Non-autonomous Notions for Borel Measures
Pramod Das, Tarun Das
TL;DR
This paper explores new concepts like expansiveness, stability, and persistence for Borel measures under dynamic maps, showing that measures with these properties are stable under certain conditions.
Contribution
It introduces and studies non-autonomous notions for Borel measures, establishing stability results for expansive persistent measures.
Findings
Expansive persistent measures are topologically stable.
New non-autonomous notions for Borel measures are defined and analyzed.
Stability results hold for measures under time varying homeomorphisms.
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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Stochastic processes and statistical mechanics