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Ferenczi, Sébastien; Holton, Charles; Zamboni, Luca Q.
Structure of three interval exchange transformations I : an arithmetic study. Annales de l'institut Fourier, 51 no. 4 (2001), p. 861-901
Full text djvu | pdf | Reviews MR 1849209 | Zbl 1029.11036 | 2 citations in Numdam
Class. Math.: 11J70, 11J13, 37A05

stable URL: http://www.numdam.org/item?id=AIF_2001__51_4_861_0

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Abstract

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 ${\Bbb Q}.$

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