Weak mixing of maps with bounded cutting parameter

2005/02/13 by El Houcein El Abdalaoui, Abdalaoui, El Houcein El, Arnaldo A. N. Noguiera +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Primary : 37D05 #math.DS #msc:37A30 #msc:37D05 #secondary : 37A30

paper · pdf · doi:10.48550/arxiv.math/0502273

2004

arxiv created 2005/02/13 · arxiv updated 2009/12/01

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 in a dynamical process called Rauzy induction.

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