New York Journal of Mathematics
Volume 11 (2005) 81-87

  

El Houcein El Abdalaoui, Arnaldo Nogueira, and Thierry de la Rue

Weak mixing of maps with bounded cutting parameter


Published: March 17, 2005
Keywords: Weak mixing, Ornstein transformations, interval exchange maps
Subject: Primary: 37D05; secondary: 37A30.

Abstract
In the class of Ornstein transformations the mixing property satisfies a 0-1 law. Here we consider Ornstein's construction with bounded cutting parameter. In fact, these latter transformations are not mixing, however it is proved that the weak mixing property occurs with probability one. Our situation is similar to the case of interval exchange transformations whose link with the cutting and stacking construction relies on a dynamical process called Rauzy induction.

Acknowledgements

The second author was partially supported by grants from CNPq-Brazil 301456/80 and FINEP/ CNPq/MCT 41.96.0923.00 (PRONEX)


Author information

El Houcein El Abdalaoui:
Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS - Université de Rouen, site Colbert , 76821 Mont-Saint-Aignan CEDEX, France
ElHocein.Elabdalaoui@univ-rouen.fr

Arnaldo Nogueira:
IML - Marseille, 163, av. de Luminy - Case 907, 13288 Marseille Cedex 9, France
nogueira@iml.univ-mrs.fr

Thierry de la Rue:
Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS - Université de Rouen, site Colbert , 76821 Mont-Saint-Aignan CEDEX, France

thierry.de-la-rue@univ-rouen.fr