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.
Hubert P., Lelievre S., Marchese L., Ulcigrai C. (2018). The lagrange spectrum of some square-tiled surfaces. ISRAEL JOURNAL OF MATHEMATICS, 225(2), 553-607 [10.1007/s11856-018-1667-3].
The lagrange spectrum of some square-tiled surfaces
Marchese L.;
2018
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
