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

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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 Teichmüller disk and prove a formula which allows to express large values in the Lagrange spectrum as sums of Cantor sets.

Original language	English
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
Publication status	Published - 2016

Keywords

Boundary expansions
Hall ray
Lagrange spectrum
Veech surfaces

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10.4171/GGD/384

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via European Mathematical Society at http://www.ems-ph.org/journals/show_abstract.php?issn=1661-7207&vol=10&iss=4&rank=8 . Please refer to any applicable terms of use of the publisher.
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AU - Marchese, Luca

AU - Ulcigrai, Corinna

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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.

KW - Boundary expansions

KW - Hall ray

KW - Lagrange spectrum

KW - Veech surfaces

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DO - 10.4171/GGD/384

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JO - Groups, Geometry and Dynamics

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The Lagrange spectrum of a Veech surface has a Hall ray

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Keywords

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