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In the paper we study aperiodic substitutional dynamical systems arisen from non-primitive substitutions. We prove that the Vershik home-omorphism ϕ of a stationary ordered Bratteli diagram is homeomorphic to an aperiodic substitutional system if and only if no restriction of ϕ to a minimal component is homeomorphic to an odometer. We also show that every(More)
This survey is focused on the results related to topologies on the groups of transformations in ergodic theory, Borel, and Cantor dynamics. Various topological properties (density, connectedness, genericity) of these groups and their subsets (subgroups) are studied. In this paper, we intend to present a unified approach to the study of topological(More)
In this paper we study ergodic measures on non-simple Bratteli diagrams of finite rank that are invariant with respect to the cofinal equivalence relation. We describe the structure of finite rank diagrams and prove that every ergodic invariant measure (finite or infinite) is an extension of a finite ergodic measure defined on a simple subdiagram. We find(More)
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