274 citations
- National Academy of Sciences of UkraineUA15 papers
- Texas A&M UniversityUS4 papers
- Kharkiv Institute of Physics and TechnologyUA3 papers
- Aston UniversityGB2 papers
- Centre National de la Recherche ScientifiqueFR2 papers
- Leiden UniversityNL2 papers
- Polish Academy of SciencesPL2 papers
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6 papers · 1 filter
Rank-one flows of transformations with infinite ergodic index
Alexandre I. Danilenko, Kyewon K. Park
A rank-one infinite measure preserving flow is constructed such that for each , the Cartesian powers of the transformation are all ergodic.
New spectral multiplicities for mixing transformations
Alexandre I. Danilenko
It is shown that if is any subset of such that either or then there is a mixing transformation whose set of spectral multiplicities is .
On new spectral multiplicities for ergodic maps
Alexandre I. Danilenko
It is shown that each subset of positive integers that contains 2 is realizable as the set of essential values of the multiplicity function for the Koopman operator of some weakly…
Invariant Measures on Stationary Bratteli Diagrams
S. Bezuglyi, J. Kwiatkowski, K. Medynets +1
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 invarian…
Almost continuous orbit equivalence for non-singular homeomorphisms
Alexandre I. Danilenko, Andrés del Junco
Let and be Polish spaces with non-atomic Borel measures and of full support. Suppose that and are ergodic non-singular homeomorphisms of and …
Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems
Sergey Bezuglyi, Konstantin Medynets
In the paper, we consider the full group and topological full group of a Cantor minimal system $(X,\f)$. We prove that the commutator subgroups $D([\f])$ and $D([[\f]…