Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transfomations

Details Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transfomations Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transfomations

2011-04-20

arxiv.org/abs/1104.3980v2

Mathematics

Dynamical Systems

Scientific paper

The two-dimensional homogeneous Euclidean algorithm is the central motivation for the definition of the classical multidimensional continued fraction algorithms, as Jacobi-Perron, Poincar\'e, Brun and Selmer algorithms. The Rauzy induction, a generalization of the Euclidean algorithm, is a key tool in the study of interval exchange transformations. Both maps are known to be dissipative and ergodic with respect to Lebesgue measure. Here we prove that they are exact.

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