# American Institute of Mathematical Sciences

January  2011, 5(1): 123-183. doi: 10.3934/jmd.2011.5.123

## The Khinchin Theorem for interval-exchange transformations

 1 Section de mathématiques, case postale 64, 2–4 Rue du Lièvre, 1211 Genève, Switzerland

Received  April 2010 Revised  December 2010 Published  April 2011

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.
Citation: Luca Marchese. The Khinchin Theorem for interval-exchange transformations. Journal of Modern Dynamics, 2011, 5 (1) : 123-183. doi: 10.3934/jmd.2011.5.123
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