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.
Artigiani M., Marchese L., Ulcigrai C. (2016). The Lagrange spectrum of a Veech surface has a Hall ray. GROUPS, GEOMETRY, AND DYNAMICS, 10(4), 1287-1337 [10.4171/GGD/384].
The Lagrange spectrum of a Veech surface has a Hall ray
Marchese L.;
2016
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.File in questo prodotto:
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