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November  2009, 24(4): 1345-1363. doi: 10.3934/dcds.2009.24.1345

Stability of invariant measures

Siniša Slijepčević 1,

1. 

Department of Mathematics, Bijenička 30, Zagreb, Croatia

Received  January 2008 Revised  December 2008 Published  May 2009

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 $p=\infty$.
Keywords: Invariant measure, exponential stability, optimal transport problem, Liapunov stability, attractors., weak* topology.
Mathematics Subject Classification: Primary: 37B25; Secondary: 37A05, 28C1.
Citation: Siniša Slijepčević. Stability of invariant measures. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1345-1363. doi: 10.3934/dcds.2009.24.1345
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