2016/02/05 by Pascal Hubert, Hubert, Pascal, Samuel Lelièvre +5
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1602.02126
openalex publication_date 2016/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.