Weak mixing of maps with bounded cutting parameter

Details Weak mixing of maps with bounded cutting parameter Weak mixing of maps with bounded cutting parameter

2005-02-13

arxiv.org/abs/math/0502273v1

Mathematics

Dynamical Systems

2004

Scientific paper

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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