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arXiv · 1704.06138

Sets of invariant measures and Cesaro stability

Sergey Kryzhevich
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Abstract

Sets of invariant measures are considered for continuous maps of a metric compact set. We take Kantorovich metric to calculate distance between measures and Hausdorff metrics to calculate distance between compact sets. Consider the function that makes correspondence between a continuous map and the set of all its Borel probability invariant measures. We demonstrate that a typical map is a continuity point of that function. Using approaches of Takens' tolerance stability theory we provide some corollaries that demonstrate that for a typical map points are structurally stable in a statistical sense.

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Sergey Kryzhevich. 2017-04-20. Sets of invariant measures and Cesaro stability. https://arxiv.org/abs/1704.06138

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