Stability of invariant measures

2008/11/01 by Siniša Slijepčević, Sinisa Slijepcevic, Slijepcevic, Sinisa
Mathematics · #37B25 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #math.DS #msc:37B25

paper · pdf · doi:10.48550/arxiv.0811.0109

arxiv created 2008/11/01 · openalex publication_date 2008/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize various notions of stability of invariant sets of dynamical systems to invariant measures, by defining a topology on the set of measures. The defined topology is similar, but not topologically equivalent to weak* topology, and it also differs from topologies induced by the Riesz Representation Theorem. It turns out that the constructed topology is a solution of a limit case of a p-optimal transport problem, for p=∞.

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