Groups, Geometry, and Dynamics

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Volume 10, Issue 4, 2016, pp. 1287–1337
DOI: 10.4171/GGD/384

Published online: 2017-01-26

The Lagrange spectrum of a Veech surface has a Hall ray

Mauro Artigiani[1], Luca Marchese[2] and Corinna Ulcigrai[3]

(1) University of Bristol, UK
(2) Universit├ę Paris 13, France
(3) University of Bristol, UK

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

Keywords: Lagrange spectrum, Veech surfaces, Hall ray, boundary expansions

Artigiani Mauro, Marchese Luca, Ulcigrai Corinna: The Lagrange spectrum of a Veech surface has a Hall ray. Groups Geom. Dyn. 10 (2016), 1287-1337. doi: 10.4171/GGD/384