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. © 2011 AIMSciences.
Marchese L. (2011). The khinchin theorem for interval-exchange transformations. JOURNAL OF MODERN DYNAMICS, 5(1), 123-183 [10.3934/jmd.2011.5.123].
The khinchin theorem for interval-exchange transformations
Marchese L.
2011
Abstract
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. © 2011 AIMSciences.File in questo prodotto:
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