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Hausdorff dimension of a class of three-interval exchange maps
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). (Dynamical Systems)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In \cite{B} Bourgain proves that Sarnak's disjointness conjecture holds for a certain class of Three-interval exchange maps. In the present paper we slightly improve the Diophantine condition of Bourgain and estimate the constants in the proof. We further show, that the new parameter set has positive, but not full Hausdorff dimension. This, in particular, implies that the Lebesgue measure of this set is zero.

Keyword [en]
Dynamical Systems, Ergodic Theory, Number Theory
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-215737OAI: oai:DiVA.org:kth-215737DiVA, id: diva2:1149255
Note

QC 20171016

Available from: 2017-10-13 Created: 2017-10-13 Last updated: 2017-10-16Bibliographically 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. p. 30
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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Citation style
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