A Gauss measure on the set of interval exchange transformations.
An interval exchange transformation is a piece-wise order-preserving isometry of a finite interval. In previous works the author has reduced certain questions about interval exchange transformations to questions about the ergodic behavior of a related class of transformations, with domain the body of all interval exchange transformations. The latter questions can be answered with the aid of Gauss measures for the related transformations; by Gauss measure is understood a conservative, ergodic invariant measure whose density is a rational function. The present note describes the construction of such Gauss measures.
Veech
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Mathematics Department, Rice University, Houston, Texas 77001.