Hausdorff dimension of a class of three-interval exchange maps

2017/01/08 by Karagulyan, Davit
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.01984

Abstract

In \citeB 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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