arXiv:2311.07208 Abstract | arXiv Analytics

arXiv:2311.07208 [math.DS]Abstract References Reviews Resources

The mean orbital pseudo-metric and the space of invariant measures

Published 2023-11-13Version 1

We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures. We give equivalent conditions for when the set of invariant measures generated by periodic points is dense in the set of ergodic measures and the space of invariant measures. We also introduce the concept of asymptotic orbital average shadowing property and show that it implies that every non-empty compact connected subset of the space of invariant measures has a generic point.

Comments: 20 pages. To appear in Acta Mathematica Sinica, English Series

Categories: math.DS

Subjects: 37B65, 37B05

Keywords: invariant measures, mean orbital pseudo-metric, asymptotic orbital average shadowing property, non-empty compact connected subset, periodic points

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