JMD
The Khinchin Theorem for interval-exchange transformations
Luca Marchese
Journal of Modern Dynamics 2011, 5(1): 123-183 doi: 10.3934/jmd.2011.5.123
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.
keywords: Rauzy– Veech induction Interval-exchange transformations Teichmüller dynamics. Diophantine conditions

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