On spectral disjointness of powers for rank-one transformations and Möbius orthogonality

DOI10.1016/j.jfa.2013.09.005zbMath1351.37048arXiv1301.0134OpenAlexW2090245114MaRDI QIDQ477038

Thierry De La Rue, El Houcein El Abdalaoui, Mariusz Lemanczyk

Publication date: 2 December 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.0134

zbMATH Keywords

Möbius functionergodicityrank-one automorphismSarnak's conjecture

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (31)

Möbius disjointness for models of an ergodic system and beyond ⋮ Möbius disjointness for homogeneous dynamics ⋮ 0-1 sequences of the Thue-Morse type and Sarnak’s conjecture ⋮ Sarnak’s conjecture for a class of rank-one subshifts ⋮ Odometers and Toeplitz systems revisited in the context of Sarnak's conjecture ⋮ Spectral properties of the Möbius function and a random Möbius model ⋮ Möbius orthogonality of sequences with maximal entropy ⋮ Möbius disjointness for analytic skew products ⋮ Möbius orthogonality for the Zeckendorf sum-of-digits function ⋮ Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures ⋮ The Möbius function and continuous extensions of rotations ⋮ Explicit rank-1 constructions for irrational rotations ⋮ Arbitrarily slow decay in the Möbius disjointness conjecture ⋮ A large class of dendrite maps for which Möbius disjointness property of Sarnak is fulfilled ⋮ Topological Wiener-Wintner ergodic theorem with polynomial weights ⋮ Substitutions and Möbius disjointness ⋮ Möbius disjointness for topological models of ergodic measure-preserving systems with quasi-discrete spectrum ⋮ Periodic codings of Bratteli-Vershik systems ⋮ Measure complexity and Möbius disjointness ⋮ Möbius disjointness conjecture for local dendrite maps ⋮ The logarithmic Sarnak conjecture for ergodic weights ⋮ Möbius disjointness for interval exchange transformations on three intervals ⋮ On Sarnak's conjecture and Veech's question for interval exchanges ⋮ Rank-one actions, their \((C, F)\)-models and constructions with bounded parameters ⋮ Hausdorff dimension of a class of three-interval exchange maps ⋮ On certain aspects of the M\"obius randomness principle ⋮ Measure-preserving rank one transformations ⋮ Disjointness of the Möbius transformation and Möbius function ⋮ Spectral disjointness of rescalings of some surface flows ⋮ Möbius orthogonality for \(q\)-semimultiplicative sequences ⋮ Spectral disjointness of powers of diffeomorphisms with arbitrary Liouvillean rotation behavior

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