The Lagrange spectrum of a Veech surface has a Hall ray

Mauro Artigiani, Luca Marchese, Corinna Ulcigrai

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)
295 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)1287-1337
Number of pages51
JournalGroups, Geometry and Dynamics
Issue number4
Publication statusPublished - 2016


  • Boundary expansions
  • Hall ray
  • Lagrange spectrum
  • Veech surfaces


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