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Information × Registration Number 0219U001824, 0118U006429 , R & D reports Title Cantor dynamical systems and their classification popup.stage_title Head Karpel Olena Mykhailivna, Registration Date 06-03-2019 Organization B.Verkin Institute for Low Temperature Physics and Engineering NAS of Ukraine popup.description2 The modelling of an arbitrary homeomorphism of a zero-dimensional compact metric space, in particular, an arbitrary homeomorphism of a Cantor space, with the help of the Vershik map acting on the path space of an ordered Bratteli diagram, is considered. The problems of non-uniqueness of the prolongation of the Vershik map from the space of all non-maximal paths of an ordered Bratteli diagram to the space of all paths is investigated. Homeomorphisms for which there exist Bratteli-Vershik models which have a unique prolongation of the Vershik map to the path space of a Bratteli diagram are characterized. Aperiodic homeomorphisms of the Cantor set are studied, a full characterization of the simplex of probability invariant measures is given in terms of incidence matrices of Bratteli diagrams, which model such homeomorphisms. For arbitrary Cantor dynamical systems of finite topological rank the methods of determining of exact number of probability ergodic invariant measures are developed, the criterion for a system to have an arbitrary given number of such measures is proved. For arbitrary aperiodic homeomorphisms of Cantor spaces sufficient conditions for them to have a given number of probability ergodic measures are also found. Product Description popup.authors Карпель Олена Михайлівна popup.nrat_date 2020-04-02 Close