de Mathématiques de Luminy
Ferenczi Sébastien, Holton
Charles and Zamboni Luca Q.
Structure of three-interval exchange transformations I : an arithmetic study
In this paper we describe a 2-dimensional generalization of the Euclidean
algorithm which stems from the dynamics of 3-interval exchange transformations.
We investigate various diophantine properties of the algorithm including
the quality of simultaneous approximations. We show it verifies the
following Lagrange type theorem: the algorithm is eventually periodic
if and only if the parameters lie in the same quadratic extension of