Stability of invariant measures

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

Stability of invariant measures

1.	Department of Mathematics, Bijenička 30, Zagreb, Croatia

Received January 2008 Revised December 2008 Published May 2009

Abstract
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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 & Continuous Dynamical Systems - A, 2009, 24 (4) : 1345-1363. doi: 10.3934/dcds.2009.24.1345

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