The Lagrange spectrum of some square-tiled surfaces
Dynamical Systems
2016-02-08 v1 Number Theory
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.
Cite
@article{arxiv.1602.02126,
title = {The Lagrange spectrum of some square-tiled surfaces},
author = {Pascal Hubert and Samuel Lelièvre and Luca Marchese and Corinna Ulcigrai},
journal= {arXiv preprint arXiv:1602.02126},
year = {2016}
}
Comments
39 pages, 7 figures