JournalsggdVol. 10, No. 4pp. 1287–1337

The Lagrange spectrum of a Veech surface has a Hall ray

  • Mauro Artigiani

    University of Bristol, UK
  • Luca Marchese

    Université Paris 13, France
  • Corinna Ulcigrai

    University of Bristol, UK
The Lagrange spectrum of a Veech surface has a Hall ray cover
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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