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On Mobius orthogonality for subshifts of finite type with positive topological entropy
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2017 (English)In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 237, no 3, 277-282 p.Article in journal (Refereed) Published
Abstract [en]

We prove that Mobius orthogonality does not hold for subshifts of finite type with positive topological entropy. This, in particular, shows that all C1+alpha surface diffeomorphisms with positive entropy correlate with the Mobius function.

Place, publisher, year, edition, pages
POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN , 2017. Vol. 237, no 3, 277-282 p.
Keyword [en]
subshifts of finite type, entropy, Mobius orthogonality
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-210404DOI: 10.4064/sm8661-10-2016ISI: 000403153500004Scopus ID: 2-s2.0-85018502389OAI: oai:DiVA.org:kth-210404DiVA: diva2:1119435
Note

QC 20170704

Available from: 2017-07-04 Created: 2017-07-04 Last updated: 2017-10-12Bibliographically approved
In thesis
1. Certain results on the Möbius disjointness conjecture
Open this publication in new window or tab >>Certain results on the Möbius disjointness conjecture
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

We study certain aspects of the Möbius randomness principle and more specifically the Möbius disjointness conjecture of P. Sarnak. In paper A we establish this conjecture for all orientation preserving circle homeomorphisms and continuous interval maps of zero entropy. In paper B we show, that for all subshifts of finite type with positive topological entropy the Möbius disjointness does not hold. In paper C we study a class of three-interval exchange maps arising from a paper of Bourgain and estimate its Hausdorff dimension. In paper D we consider the Chowla and Sarnak conjectures and the Riemann hypothesis for abstract sequences and study their relationship.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2017. 30 p.
Series
TRITA-MAT-A, 2017:05
Keyword
Dynamical Systems, Ergodic Theory, Number Theory
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-215682 (URN)978-91-7729-561-7 (ISBN)
Public defence
2017-11-03, F3, Kungl Tekniska högskolan, Lindstedtsvägen 26,, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20171016

Available from: 2017-10-16 Created: 2017-10-12 Last updated: 2017-10-16Bibliographically approved

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Karagulyan, Davit

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