Weak Mixing in Interval Exchange Transformations of Periodic Type |
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| Authors: | YA.?G.?Sinai mailto:sinai@math.princeton.edu" title=" sinai@math.princeton.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,C.?Ulcigrai |
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| Affiliation: | (1) Mathematics Department, Princeton University, Washington Road, Princeton, NJ 08544-1000, USA;(2) Landau Institute of Theoretical Physics, Russian Academy of Sciences, 2 Kosygin Street, 117334 Moscow, Russia |
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| 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. *Dedicated to the memory of F.A. Berezin |
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| Keywords: | interval exchange transformations weak mixing spectral measures |
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