The Lagrange spectrum of a Veech surface has a Hall ray

Mauro Artigiani; Luca Marchese; Corinna Ulcigrai

doi:10.4171/GGD/384

The Lagrange spectrum of a Veech surface has a Hall ray

Mauro Artigiani
, Luca Marchese
, Corinna Ulcigrai

Producción científica: Contribución a revista › Artículo de Investigación › revisión exhaustiva

9 Citas (Scopus)

Resumen

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.

Idioma original	Inglés estadounidense
Páginas (desde-hasta)	1287-1337
Número de páginas	51
Publicación	Groups, Geometry, and Dynamics
Volumen	10
N.º	4
DOI	https://doi.org/10.4171/GGD/384
Estado	Publicada - 2016
Publicado de forma externa	Sí

Áreas temáticas de ASJC Scopus

Geometría y topología
Matemáticas discretas y combinatorias

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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 Teichm{\"u}ller disk and prove a formula which allows to express large values in the Lagrange spectrum as sums of Cantor sets.",

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N2 - 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.

AB - 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.

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AN - SCOPUS:85013893882

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The Lagrange spectrum of a Veech surface has a Hall ray

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