Abstract: | For any ergodic transformation T of a Lebesgue space (X, μ), it is possible to introduce a topology τ on X such that (a) X becomes a totally disconnected compactum (a Cantor set) with a Markov structure, and μ becomes a Borel Markov measure;
(b) T becomes a minimal strictly ergodic homeomorphism of (X, τ); (c) the orbit partition of T is the tail partition of the Markov compactum (up to two classes of the partition). The Markov
compactum structure is the same as the path structure of the Bratteli diagram for some AF-algebra. Bibliography: 19 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 223, 1995, pp. 120–126. |