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Topological dichotomy and strict ergodicity for translation surfaces

Published online by Cambridge University Press:  15 October 2008

YITWAH CHEUNG,
PASCAL HUBERT and
HOWARD MASUR
YITWAH CHEUNG
Affiliation:
San Francisco State University, San Francisco, CA 94132, USA (email: cheung@math.sfsu.edu)
PASCAL HUBERT
Affiliation:
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)
HOWARD MASUR
Affiliation:
University of Illinois at Chicago, Chicago, IL 60607, USA (email: masur@math.uic.edu)
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 6 , December 2008, pp. 1729 - 1748
Copyright
Copyright © 2008 Cambridge University Press

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