Invariant measures for Cantor dynamical systems

S Bezuglyi; O Karpel

doi:10.48550/arXiv.1904.09666

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Invariant measures for Cantor dynamical systems

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Invariant measures for Cantor dynamical systems

S Bezuglyi and O Karpel

ArXiv.org

04/21/2019

DOI: 10.48550/arXiv.1904.09666

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https://doi.org/10.48550/arXiv.1904.09666View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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.

Details

Title: Subtitle: Invariant measures for Cantor dynamical systems
Creators: S Bezuglyi
O Karpel
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arXiv.1904.09666
ISSN: 2331-8422
Language: English
Date posted: 04/21/2019
Academic Unit: Mathematics
Record Identifier: 9984240874402771

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