TY - JOUR
T1 - The Lagrange spectrum of some square-tiled surfaces
AU - Hubert, Pascal
AU - Lelievere, Samuele
AU - Marchese, Luca
AU - Ulcigrai, Corinna
PY - 2018/4/11
Y1 - 2018/4/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85047454023&partnerID=8YFLogxK
U2 - 10.1007/s11856-018-1667-3
DO - 10.1007/s11856-018-1667-3
M3 - Article (Academic Journal)
AN - SCOPUS:85047454023
SN - 0021-2172
VL - 225
SP - 553
EP - 607
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -