### 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 language | English (US) |
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Pages (from-to) | 111-133 |

Number of pages | 23 |

Journal | Letters in Mathematical Physics |

Volume | 74 |

Issue number | 2 |

DOIs | |

State | Published - 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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## Cite this

Sinai, Y. G., & Ulcigrai, C. (2005). Weak mixing in interval exchange transformations of periodic type.

*Letters in Mathematical Physics*,*74*(2), 111-133. https://doi.org/10.1007/s11005-005-0011-0