Veech's dichotomy and the lattice property

John Smillie, Barak Weiss

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume28
Issue number6
DOIs
StatePublished - Dec 2008
Externally publishedYes

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