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Sets of invariant measures and Cesaro stability by Kryzhevich, Sergey is a scholarly article available to read on EtoBox.

What is Sets of invariant measures and Cesaro stability about?

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.

Author

Kryzhevich, Sergey

Published

2017

Language

EN