Veech's dichotomy and the lattice property

John Smillie, Barak Weiss

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Veech showed that if a translation surface has a stabilizer which is a lattice in SL(2,ℝ), 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.

Original languageEnglish
Pages (from-to)1959-1972
Number of pages14
JournalErgodic Theory and Dynamical Systems
Issue number6
StatePublished - 1 Dec 2008

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'Veech's dichotomy and the lattice property'. Together they form a unique fingerprint.

Cite this