The Lagrange spectrum of some square-tiled surfaces

Pascal Hubert, Samuele Lelievere, Luca Marchese, Corinna Ulcigrai

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
172 Downloads (Pure)

Abstract

Lagrange spectra have been defined for closed submanifolds of the moduli space of translation surfaces which are invariant under the action of SL(2, ℝ). We consider the closed orbit generated by a specific covering of degree 7 of the standard torus, which is an element of the stratum H(2). We give an explicit formula for the values in the spectrum, in terms of a cocycle over the classical continued fraction. Differently from the classical case of the modular surface, where the lowest part of the Lagrange spectrum is discrete, we find an isolated minimum, and a set with a rich structure right above it.

Original languageEnglish
Pages (from-to)553-607
Number of pages55
JournalIsrael Journal of Mathematics
Volume225
Issue number2
DOIs
Publication statusPublished - 11 Apr 2018

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