Structure of three interval exchange transformations. I: An arithmetic study (Q5944297)

The authors introduce a 2-dimensional division algorithm coming from the dynamics of a three interval exchange transformation on the unit circle. This algorithm is called ``the negative slope algorithm''. It is based upon a two-dimensional generalization of the Gauss map. In this paper the authors study Diophantine approximation properties of this algorithm. As a consequence they show, in particular, that the Gauss-like map underlying this algorithm satisfies a Lagrange type theorem.