Displaying similar documents to “Discrete planes, 2 -actions, Jacobi-Perron algorithm and substitutions”

Structure of three interval exchange transformations I: an arithmetic study

Sébastien Ferenczi, Charles Holton, Luca Q. Zamboni (2001)

Annales de l’institut Fourier

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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 .