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Joinings of three-interval exchange transformations

Published online by Cambridge University Press:  02 February 2005

SÉBASTIEN FERENCZI ,
CHARLES HOLTON  and
LUCA Q. ZAMBONI
SÉBASTIEN FERENCZI
Affiliation:
Institut de Mathématiques de Luminy, CNRS-UPR 9016, Case 907, 163 av. de Luminy, F13288 Marseille Cedex 9, France and Fédération de Recherche des Unités de Mathématiques de Marseille, CNRS-FR 2291, France (e-mail: ferenczi@iml.univ-mrs.fr)
CHARLES HOLTON
Affiliation:
Department of Mathematics RLM 8.100, University of Texas at Austin, 26th and Speedway, Austin, TX 78712-1082, USA (e-mail: cholton@math.utexas.edu)
LUCA Q. ZAMBONI
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-5116, USA (e-mail: luca@unt.edu)
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Abstract

We show that among three-interval exchange transformations there exists a dichotomy: T has minimal self-joinings whenever the associated subshift is linearly recurrent, and is rigid otherwise. We also build a family of simple rigid three-interval exchange transformations, which is a step towards an old question of Veech, and a family of rigid three-interval exchange transformations, which includes Katok's rank-one map.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 2 , April 2005 , pp. 483 - 502
Copyright
2005 Cambridge University Press

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