Khinchin theorem for interval exchange transformations

Details Khinchin theorem for interval exchange transformations Khinchin theorem for interval exchange transformations

2010-03-30

arxiv.org/abs/1003.5883v2

Mathematics

Dynamical Systems

53 pages

Scientific paper

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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