The Lagrange spectrum of a Veech surface has a Hall ray

2014/09/24 by Artigiani, Mauro, Marchese, Luca, Ulcigrai, Corinna
#11J06 #37D40 (Primary) 32G15 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1409.7023

Abstract

We study Lagrange spectra of Veech translation surfaces, which are a generalization of the classical Lagrange spectrum. We show that any such Lagrange spectrum contains a Hall ray. As a main tool, we use the boundary expansion developed by Bowen and Series to code geodesics in the corresponding Teichmüller disk and prove a formula which allows to express large values in the Lagrange spectrum as sums of Cantor sets.

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