a1 Department of Mathematics, Cornell University, Ithaca, NY, USA (email: email@example.com)
a2 Department of Mathematics, Ben Gurion University, Be’er Sheva, 84105, Israel (email: firstname.lastname@example.org)
Veech showed that if a translation surface has a stabilizer which is a lattice in SL(2,), then any direction for the corresponding constant slope flow is either completely periodic or uniquely ergodic. We show that the converse does not hold: there are translation surfaces that satisfy Veech’s dichotomy but for which the corresponding stabilizer subgroup is not a lattice. The construction relies on work of Hubert and Schmidt.
(Received July 27 2006)
(Revised January 22 2008)