23 citations · 98 across the 23 of their papers we have counts for
24 papers
Unveiling universality, encloseness, and orthogonality in dynamics
J. Aaronson, A. I. Danilenko, J. Kułaga-Przymus +1
Motivated by Sarnak's conjecture on Möbius orthogonality, we investigate the general problem of orthogonality for a bounded sequence to topological models of characteristic classes…
A note on -free sets and the existence of natural density
Aurelia Dymek, Stanisław Kasjan, Joanna Kułaga-Przymus
Given , let be the correspoding set of multiples. We say that is taut…
Basic thermodynamical formalism for sandwich subshifts
Joanna Kułaga-Przymus, Michał D. Lemańczyk, Michał Rams
Consider a partial order on when for all . A subshift is hereditary if together with any…
Invariant measures for -free systems revisited
Aurelia Dymek, Joanna Kułaga-Przymus, Daniel Sell
For , the -free subshift is the orbit closure of the characteristic function of the set of -free integers.…
Minimality of -free systems in number fields
Aurelia Dymek, Stanisław Kasjan, Joanna Kułaga-Przymus
Let be a finite extension of and be its ring of integers. Let be a primitive collection of ideals in . We show that a…
On arithmetic functions orthogonal to deterministic sequences
Adam Kanigowski, Joanna Kulaga-Przymus, Mariusz Lemańczyk +1
We prove Veech's conjecture on the equivalence of Sarnak's conjecture on Möbius orthogonality with a Kolmogorov type property of Furstenberg systems of the M\''obius function. This…
Sarnak's Conjecture from the Ergodic Theory Point of View
Joanna Kułaga-Przymus, Mariusz Lemańczyk
This is a survey on Sarnak's Conjecture
Entropy rate of product of independent processes
Joanna Kułaga-Przymus, Michał Lemańczyk
We study the multiplicative version of the classical Furstenberg's filtering problem, where instead of the sum one considers the product $\mathbf{X}\cdot \m…
Hereditary subshifts whose measure of maximal entropy has no Gibbs property
Joanna Kułaga-Przymus, Michał Lemańczyk
We show that the measure of maximal entropy for the hereditary closure of a -free subshift has the Gibbs property if and only if the Mirsky measure of the subshift is…
Sarnak's Conjecture -- what's new
S. Ferenczi, J. Kułaga-Przymus, M. Lemańczyk
An overview of last seven years results concerning Sarnak's conjecture on Möbius disjointness is presented, focusing on ergodic theory aspects of the conjecture.
A structure theorem for level sets of multiplicative functions and applications
Vitaly Bergelson, Joanna Kułaga-Przymus, Mariusz Lemańczyk +1
Given a level set of an arbitrary multiplicative function , we establish, by building on the fundamental work of Frantzikinakis and Host [13,14], a structure theorem which g…
Möbius disjointness for models of an ergodic system and beyond
El Houcein El Abdalaoui, Joanna Kułaga-Przymus, Mariusz Lemańczyk +1
Given a topological dynamical system and an arithmetic function , we study the strong MOMO property (relatively to $\boldsymbol…
Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics
Vitaly Bergelson, Joanna Kułaga-Przymus, Mariusz Lemańczyk +1
A set is called rational if it is well-approximable by finite unions of arithmetic progressions. Examples of rational sets include many classical sets of numb…
Approximate orthogonality of powers for ergodic affine unipotent diffeomorphisms on nilmanifolds
Livio Flaminio, Krzysztof Frączek, Joanna Kułaga-Przymus +1
Let be a connected, simply connected nilpotent Lie group and a lattice. We prove that each ergodic diffeomorphism on the nilmanifold , where $…
Multiple mixing and parabolic divergence in smooth area-preserving flows on higher genus surfaces
Adam Kanigowski, Joanna Kułaga-Przymus, Corinna Ulcigrai
We consider typical area preserving flows on higher genus surfaces and prove that the flow restricted to mixing minimal components is mixing of all orders, thus answering affimativ…
-free sets and dynamics
Aurelia Bartnicka, Stanisław Kasjan, Joanna Kułaga-Przymus +1
Let and let be the characteristic function of the set of B-free numbers. Consider $…
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…
-free integers in number fields and dynamics
Francisco Araújo, Aurelia Dymek, Joanna Kułaga-Przymus
In 2010, Sarnak initiated the study of the dynamics of the system determined by the square of the Möbius function (the characteristic function of the square-free integers). We deal…
The Chowla and the Sarnak conjectures from ergodic theory point of view
El Houcein El Abdalaoui, Joanna Kulaga-Przymus, Mariusz Lemanczyk +1
We rephrase the conditions from the Chowla and the Sarnak conjectures in abstract setting, that is, for sequences of numbers in {-1,0,1}, and introduce several natural generalizati…
On invariant measures for -free systems
Joanna Kułaga-Przymus, Mariusz Lemańczyk, Benjamin Weiss
We show that the -free subshift associated to a -free system is intrinsically ergodic, i.e.\ it has exactly one measure of maximal e…
On embeddability of automorphisms into measurable flows from the point of view of self-joining properties
Joanna Kułaga-Przymus
We compare self-joining- and embeddability properties. In particular, we prove that a measure preserving flow with ergodic is 2-fold quasi-simple (2-…
On the strong convolution singularity property
Joanna Kułaga-Przymus
We develop a new method for proving that a flow has the so-called strong convolution singularity property, i.e. the Gaussian system induced by its (reduced) maximal spectral type h…
Non-reversibility and self-joinings of higher orders for ergodic flows
K. Fraczek, J. Kulaga, M. Lemanczyk
By studying the weak closure of multidimensional off-diagonal self-joinings we provide a criterion for non-isomorphism of a flow with its inverse, hence the non-reversibility of a…