The Lagrange spectrum of a Veech surface has a Hall ray | Zendy

Mauro Artigiani | Zendy; Luca Marchese | Zendy; Corinna Ulcigrai | Zendy

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The Lagrange spectrum of a Veech surface has a Hall ray

Author(s) -

Mauro Artigiani,

Luca Marchese,

Corinna Ulcigrai

Publication year - 2017

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/384

Subject(s) - mathematics , spectrum (functional analysis) , surface (topology) , pure mathematics , algebra over a field , mathematical analysis , geometry , physics , quantum mechanics

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

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