The Lagrange spectrum of some square-tiled surfaces

  • Pascal Hubert
  • Samuel Lelièvre
  • Luca Marchese
  • Corinna Ulcigrai
Article
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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.

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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  • Pascal Hubert
    • 1
  • Samuel Lelièvre
    • 2
  • Luca Marchese
    • 3
  • Corinna Ulcigrai
    • 4
  1. 1.I2M, Centre de Mathématiques et Informatique (CMI)Université Aix-MarseilleMarseille Cedex 13France
  2. 2.Laboratoire de mathématique d’Orsay, UMR 8628 CNRS Université Paris-SudOrsay cedexFrance
  3. 3.Université Paris 13, Sorbonne Paris Cité, LAG A, UMR 7539VilletaneuseFrance
  4. 4.School of MathematicsUniversity of Bristol, University WalkClifton, BristolUK

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