Ergodic Theory and Dynamical Systems

Research Article

Topological dichotomy and strict ergodicity for translation surfaces

YITWAH CHEUNGa1, PASCAL HUBERTa2 and HOWARD MASURa3

a1 San Francisco State University, San Francisco, CA 94132, USA (email: cheung@math.sfsu.edu)

a2 LATP, Case cour A, Faculté des Sciences de Saint Jérôme, Avenue Escadrille Normandie-Niemen, 13397, Marseille Cedex 20, France (email: hubert@cmi.univ-mrs.fr)

a3 University of Illinois at Chicago, Chicago, IL 60607, USA (email: masur@math.uic.edu)

Abstract

In this paper the authors find examples of translation surfaces that have infinitely generated Veech groups, satisfy the topological dichotomy property that for every direction the flow in that direction is either completely periodic or minimal, and yet have minimal but non-uniquely ergodic directions.

(Received July 01 2006)

(Revised October 01 2007)