2019/04/21 by Sergey Bezuglyi, Bezuglyi, S., Olena Karpel +1 · 1 citation
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Cellular Automata and Applications #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1904.09666
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.