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arXiv · 1104.3980

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

Tomasz Miernowski·Arnaldo Nogueira
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Abstract

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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Tomasz Miernowski, Arnaldo Nogueira. 2011-04-20. Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transfomations. https://arxiv.org/abs/1104.3980

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