Zobrazeno 1 - 10
of 246
pro vyhledávání: '"Lemańczyk, M."'
An overview of last seven years results concerning Sarnak's conjecture on M\"obius disjointness is presented, focusing on ergodic theory aspects of the conjecture.
Comment: 65 pages
Comment: 65 pages
Externí odkaz:
http://arxiv.org/abs/1710.04039
Publikováno v:
Discrete and Continuous Dynamical Systems, Volume 39 (2019), Number 5, pp. 2581-2612
We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of K\'atai's orthogonality criterion. Here is a spe
Externí odkaz:
http://arxiv.org/abs/1705.07322
We show that Sarnak's conjecture on M\"obius disjointness holds for all subshifts given by bijective substitutions and some other similar dynamical systems, e.g.\ those generated by Rudin-Shapiro type sequences.
Comment: 26 pages
Comment: 26 pages
Externí odkaz:
http://arxiv.org/abs/1507.01123
Autor:
ter Elst, A. F. M., Lemanczyk, M.
We characterize Koopman one-parameter $C_0$-groups in the class of all unitary one-parameter $C_0$-groups on $L_2(X)$ as those that preserve $L_\infty(X)$ and for which the infinitesimal generator is a derivation on the bounded functions in its domai
Externí odkaz:
http://arxiv.org/abs/1504.06008
Publikováno v:
J. Anal. Math. 122 (2014), 163-227
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 flow. This is applied to special flows over rigid automorphisms. In pa
Externí odkaz:
http://arxiv.org/abs/1206.3053
Publikováno v:
Ergod. Th. Dynam. Sys. 34 (2014) 1464-1502
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main focus in t
Externí odkaz:
http://arxiv.org/abs/1103.0905
Autor:
Lemanczyk, M., Parreau, F.
We study the problem of lifting various mixing properties from a base automorphism $T\in {\rm Aut}\xbm$ to skew products of the form $\tfs$, where $\va:X\to G$ is a cocycle with values in a locally compact Abelian group $G$, $\cs=(S_g)_{g\in G}$ is a
Externí odkaz:
http://arxiv.org/abs/1102.0848
Autor:
Abdalaoui, E. H. El, Lemanczyk, M.
For some countable discrete torsion Abelian groups we give examples of their finite measure-preserving actions which have simple spectrum and no approximate transitivity property.
Comment: 9 pages, Key words and phrases: ergodic theory, dynamica
Comment: 9 pages, Key words and phrases: ergodic theory, dynamica
Externí odkaz:
http://arxiv.org/abs/1004.0940
Autor:
Fraczek, K., Lemanczyk, M.
We consider special flows over two-dimensional rotations by $(\alpha,\beta)$ on $\T^2$ and under piecewise $C^2$ roof functions $f$ satisfying von Neumann's condition $\int_{\T^2}f_x(x,y)\,dx\,dy\neq 0\neq \int_{\T^2}f_y(x,y)\,dx\,dy.$ Such flows are
Externí odkaz:
http://arxiv.org/abs/1002.2734
We give a condition on a piecewise constant roof function and an irrational rotation by $\alpha$ on the circle to give rise to a special flow having the mild mixing property. Such flows will also satisfy Ratner's property. As a consequence we obtain
Externí odkaz:
http://arxiv.org/abs/math/0703752