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The Khinchin Theorem for interval-exchange transformations

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  • We define a Diophantine condition for interval-exchange transformations. When the number of intervals is two, that is, for rotations on the circle, our condition coincides with the classical Khinchin condition. We prove for interval-exchange transformations the same dichotomy as in the Khinchin Theorem. We also develop several results relating the Rauzy-Veech algorithm with homogeneous approximations for interval-exchange transformations.
    Mathematics Subject Classification: Primary: 37A20, 37E05; Secondary: 32G15, 11K55.


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