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

Research output: Contribution to journal › Research Article › peer-review

9 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 language	English (US)
Pages (from-to)	1287-1337
Number of pages	51
Journal	Groups, Geometry, and Dynamics
Volume	10
Issue number	4
DOIs	https://doi.org/10.4171/GGD/384
State	Published - 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/GGD/384

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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.",

author = "Mauro Artigiani and Luca Marchese and Corinna Ulcigrai",

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AU - Marchese, Luca

AU - Ulcigrai, Corinna

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Y1 - 2016

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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DO - 10.4171/GGD/384

M3 - Research Article

AN - SCOPUS:85013893882

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JO - Groups, Geometry, and Dynamics

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IS - 4

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The Lagrange spectrum of a Veech surface has a Hall ray

Abstract

All Science Journal Classification (ASJC) codes

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