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Invariant measures for Cantor dynamical systems
Conference proceeding   Open access   Peer reviewed

Invariant measures for Cantor dynamical systems

Sergey Bezuglyi and Olena Karpel
DYNAMICS: TOPOLOGY AND NUMBERS, Vol.744, pp.259-295
Contemporary Mathematics
01/01/2020
DOI: 10.1090/conm/744/14988
url
https://doi.org/10.1090/conm/744/14988View
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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.
Mathematics Physical Sciences Science & Technology

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