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arXiv · 1904.09666

Invariant measures for Cantor dynamical systems

S. Bezuglyi·O. Karpel
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Abstract

This paper is a survey devoted to the study of probability and infinite ergodic invariant measures for aperiodic homeomorphisms of a Cantor set. We focus mostly on the cases when a homeomorphism has either a unique ergodic invariant measure or finitely many such measures (finitely ergodic homeomorphisms). Since every Cantor dynamical system $(X,T)$ can be realized as a Vershik map acting on the path space of a Bratteli diagram, we use combinatorial methods developed in symbolic dynamics and Bratteli diagrams during the last decade to study the simplex of invariant measures.

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BibTeXRIS

S. Bezuglyi, O. Karpel. 2019-04-21. Invariant measures for Cantor dynamical systems. https://arxiv.org/abs/1904.09666

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