Invariant measures for Cantor dynamical systems
Dynamical Systems
2019-07-03 v1 Functional Analysis
Operator Algebras
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 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.
Cite
@article{arxiv.1904.09666,
title = {Invariant measures for Cantor dynamical systems},
author = {S. Bezuglyi and O. Karpel},
journal= {arXiv preprint arXiv:1904.09666},
year = {2019}
}
Comments
37 pages, 2 figures. arXiv admin note: text overlap with arXiv:1709.00055, arXiv:1503.03360