The Lagrange spectrum of a Veech surface has a Hall ray

Mauro Artigiani, Luca Marchese, Corinna Ulcigrai

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1287-1337
Number of pages51
JournalGroups, Geometry, and Dynamics
Volume10
Issue number4
DOIs
StatePublished - 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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