The Lagrange spectrum of a Veech surface has a Hall ray
Mauro Artigiani
University of Bristol, UKLuca Marchese
Université Paris 13, FranceCorinna Ulcigrai
University of Bristol, UK
![The Lagrange spectrum of a Veech surface has a Hall ray cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ggd-volume-10-issue-4.png&w=3840&q=90)
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.
Cite this article
Mauro Artigiani, Luca Marchese, Corinna Ulcigrai, The Lagrange spectrum of a Veech surface has a Hall ray. Groups Geom. Dyn. 10 (2016), no. 4, pp. 1287–1337
DOI 10.4171/GGD/384