Letters in Mathematical Physics

, Volume 74, Issue 2, pp 111–133 | Cite as

Weak Mixing in Interval Exchange Transformations of Periodic Type

  • YA. G. Sinai
  • C. Ulcigrai


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.


interval exchange transformations weak mixing spectral measures 

Mathematics Subject Classifications (2000)

37A05 37E05 37A30 


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© Springer 2005

Authors and Affiliations

  1. 1.Mathematics DepartmentPrinceton UniversityPrincetonUSA
  2. 2.Landau Institute of Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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