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Every ergodic transformation is disjoint from almost every interval exchange transformation. (English) Zbl 1243.37002

A very strong disjointness result is found for interval exchanges, using a criterion of F. Hahn and W. Parry [“Some characteristic properties of dynamical systems with quasi-discrete spectra”, Math. Syst. Theory 2, 179–190 (1968; Zbl 0167.32902)], which shows that if two ergodic measure-preserving transformations are spectrally singular modulo the constants then they are disjoint, and extending a result of W. A. Veech [“The metric theory of interval exchange transformations. I: Generic spectral properties”, Am. J. Math. 106, 1331–1359 (1984; Zbl 0631.28006)] on rigidity sequences for interval exchanges. The main result is that every measure-preserving transformation is disjoint from almost every interval exchange. One of the many consequences is that the product of almost any two interval exchanges is uniquely ergodic, and almost every pair of interval exchanges is disjoint.

MSC:

37A05 Dynamical aspects of measure-preserving transformations
28D05 Measure-preserving transformations
37A99 Ergodic theory
37A25 Ergodicity, mixing, rates of mixing
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References:

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