The adic realizations of the ergodic actions with the homeomorphisms of the Markov compact and the ordered Bratteli diagrams

A. M. Vershik

Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Tome 223 (1995), pp. 120-126

Résumé

For any ergodic transformation $T$ of the Lebesgue space $(X,\mu)$ it is possible to introduce the topology $\tau$ into $X$ such that a) with provided topology $X$ becomes the totally disconnected compact (Cantor set) with the structure of a Markov compact and $\mu$ becomes a Borel Markov measure. b) $T$ becomes a minimal strictly ergodic homeomorphism of $(X,\tau)$; c) orbit partition of $T$ is the tail partition of the Markov compact upto two classes of the partition. The structure of Markov compact is the same as a structure of the pathes in the Bratteli diagram of some $AF$-algebra. Bibliography: 19 titles.