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El Houcein El Abdalaoui, Arnaldo Nogueira, and Thierry de la Rue
Weak mixing of maps with bounded cutting parameter
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| Published: |
March 17, 2005
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| Keywords: |
Weak mixing, Ornstein transformations, interval exchange maps |
| Subject: |
Primary: 37D05; secondary: 37A30. |
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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.
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| Acknowledgements
The second author was partially supported by grants from CNPq-Brazil 301456/80 and FINEP/ CNPq/MCT 41.96.0923.00 (PRONEX)
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| 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
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