Invariant measures for Cantor dynamical systems

Autor:	Bezuglyi, S., Karpel, O.
Rok vydání:	2019
Předmět:	Mathematics - Dynamical Systems Mathematics - Functional Analysis Mathematics - Operator Algebras 37A05 37B05 37B10 (Primary) 28D05 28C15 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 37 pages, 2 figures. arXiv admin note: text overlap with arXiv:1709.00055, arXiv:1503.03360
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1904.09666 Zobrazit plný text záznamu View this record from Arxiv