Weak Mixing in Interval Exchange Transformations of Periodic Type
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Interval exchange transformations (IETs) are piecewise isometries of the interval, obtained permuting a certain number of subintervals. We give a condition on IETs in the special subclass of IETs with periodic Rauzy-Veech cocycle which guarantees weak mixing, i.e. the continuity of the spectrum. The proof involves the study of the associated spectral measures. The condition can be checked explicitly by computing a certain Galois group of a field related to the Ravzy-Veech cocycle. Explicit examples of weakly mixing IETs are constructed in the Appendix.
Keywordsinterval exchange transformations weak mixing spectral measures
Mathematics Subject Classifications (2000)37A05 37E05 37A30
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