Weak mixing in interval exchange transformations of periodic type

Ya G. Sinai, C. Ulcigrai

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)111-133
Number of pages23
JournalLetters in Mathematical Physics
Volume74
Issue number2
DOIs
StatePublished - Nov 1 2005

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Interval exchange transformations
  • Spectral measures
  • Weak mixing

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