Hausdorff dimension of a class of three-interval exchange maps

Davit Karagulyan

doi:10.3934/dcds.2020077

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2020, Volume 40, Issue 3: 1257-1281. Doi: 10.3934/dcds.2020077

This issue Previous Article Next Article Global well-posedness and existence of the global attractor for the Kadomtsev-Petviashvili Ⅱ equation in the anisotropic Sobolev space

Hausdorff dimension of a class of three-interval exchange maps

Davit Karagulyan

University of Maryland, Department of Mathematics, College Park, MD 20742, USA

Received: February 28, 2018

Revised: July 31, 2019

Published: December 2019

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Abstract

In [5] 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.

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Mathematics Subject Classification: Primary: 37B10, 54H20; Secondary: 28A80.

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