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 2005 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
Keywords
- Interval exchange transformations
- Spectral measures
- Weak mixing