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Structure of three interval exchange transformations. I: An arithmetic study. (English) Zbl 1029.11036

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.

MSC:

11J70 Continued fractions and generalizations
11J13 Simultaneous homogeneous approximation, linear forms
37A05 Dynamical aspects of measure-preserving transformations
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