Khinchin theorem for interval exchange transformations

Luca Marchese

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arXiv · 1003.5883

Khinchin theorem for interval exchange transformations

Luca Marchese

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Abstract

We define a diophantine condition for interval exchange transformations (i.e.t.s). When the number of intervals is two, that is for rotations on the circle, our condition coincides with classical Khinchin condition. We prove for i.e.t.s the same dichotomy as in Khinchin Theorem. We also develop several results relating the Rauzy-Veech algorithm with homogeneous approximations for i.e.t.s.

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Luca Marchese. 2010-03-30. Khinchin theorem for interval exchange transformations. https://arxiv.org/abs/1003.5883

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