Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T05:04:58.106Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected])
CHARLES HOLTON
Affiliation:
Department of Mathematics RLM 8.100, University of Texas at Austin, 26th and Speedway, Austin, TX 78712-1082, USA (e-mail: [email protected])
LUCA Q. ZAMBONI
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-5116, USA (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)