arXiv:0811.0109 Abstract | arXiv Analytics

arXiv:0811.0109 [math.DS]Abstract References Reviews Resources

Stability of invariant measures

Published 2008-11-01Version 1

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 $p=\infty$.

Categories: math.DS

Subjects: 37B25

Keywords: invariant measures, optimal transport problem, riesz representation theorem, limit case, invariant sets

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