Geodesic
The Lagrange spectrum of a Veech surface has a Hall ray
Mauro Artigiani1 ; Luca Marchese2 ; Corinna Ulcigrai1
1University of Bristol, UK
2Université Paris 13, France
Groups, geometry, and dynamics, Tome 10 (2016) no. 4, pp. 1287-1337

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DOI

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.
DOI : 10.4171/ggd/384
Classification : 11-XX, 32-XX, 37-XX
Mots-clés : Lagrange spectrum, Veech surfaces, Hall ray, boundary expansions

Mauro Artigiani  1   ; Luca Marchese  2   ; Corinna Ulcigrai  1

1 University of Bristol, UK
2 Université Paris 13, France 
Mauro Artigiani; Luca Marchese; Corinna Ulcigrai. The Lagrange spectrum of a Veech surface has a Hall ray. Groups, geometry, and dynamics, Tome 10 (2016) no. 4, pp. 1287-1337. doi: 10.4171/ggd/384
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     title = {The {Lagrange} spectrum of a {Veech} surface has a {Hall} ray},
     journal = {Groups, geometry, and dynamics},
     pages = {1287--1337},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/384/}
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