5 citations · 10 across the 4 of their papers we have counts for
5 papers
M{ö}bius orthogonality in density for zero entropy dynamical systems
Alexander Gomilko, Mariusz Lemańczyk, Thierry de La Rue
It is proved that whenever a zero entropy dynamical system has only countably many ergodic measures and stands for the arithmetic M{ö}bius function, then there exists a…
Sarnak's conjecture implies the Chowla conjecture along a subsequence
Alexander Gomilko, Dominik Kwietniak, Mariusz Lemańczyk
We show that the Möbius disjointess of zero entropy dynamical systems implies the existence of an increasing sequence of positive integers along which the Chowla conjecture on auto…
Flows with Ratner's property have discrete essential centralizer
Adam Kanigowski, Mariusz Lemańczyk
We show that a free, ergodic action of with (finite) Ratner's property has countable discrete essential centralizer. Moreover we show that such flows are mildly mixing…
Substitutions and Möbius disjointness
S. Ferenczi, J. Kułaga-Przymus, M. Lemańczyk +1
We show that Sarnak's conjecture on Möbius disjointness holds for all subshifts given by bijective substitutions and some other similar dynamical systems, e.g.\ those generated by…
Hereditary subshifts whose simplex of invariant measures is Poulsen
Joanna Kułaga-Przymus, Mariusz Lemańczyk, Benjamin Weiss
We give a sufficient condition for the simplex of invariant measures for a hereditary system to be Poulsen. In particular, we show that this simplex is Poulsen in case of positive…