# American Institute of Mathematical Sciences

March  2020, 40(3): 1257-1281. doi: 10.3934/dcds.2020077

## Hausdorff dimension of a class of three-interval exchange maps

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

Received  March 2018 Revised  August 2019 Published  December 2019

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.

Citation: Davit Karagulyan. Hausdorff dimension of a class of three-interval exchange maps. Discrete & Continuous Dynamical Systems, 2020, 40 (3) : 1257-1281. doi: 10.3934/dcds.2020077
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Khintchine spectrum
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