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.
The khinchin theorem for interval-exchange transformations / Marchese L.. - In: JOURNAL OF MODERN DYNAMICS. - ISSN 1930-5311. - STAMPA. - 5:1(2011), pp. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
