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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… (More)

In the paper we completely describe characters (central positive-definite functions) of simple locally finite groups that can be represented as inductive limits of (products of) symmetric groups… (More)

- María Isabel Cortez, Konstantin Medynets
- J. London Math. Society
- 2016

We consider infinite measure-preserving non-primitive selfsimilar tiling systems in Euclidean space R. We establish the secondorder ergodic theorem for such systems. The speed of convergence is… (More)

We continue the study of topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology τ , which was started by Bezuglyi, Dooley,… (More)

We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to… (More)

We prove that the only finite factor-representations of the HigmanThompson groups {Fn,r}, {Gn,r} are the regular representations and scalar representations arising from group abelianizations. As a… (More)

We consider the full group [φ] and topological full group [[φ]] of a Cantor minimal system (X, φ). We prove that the commutator subgroups D([φ]) and D([[φ]]) are simple and show that the groups… (More)