Institut de Mathématiques de Luminy

Abstract 2001-10

Arnoux Pierre, Berthé Valérie and Ito Shunji.
Discrete planes, Z2-action, Jacobi-Peron algorithm and substitutions.

We introduce two-dimensional substitutions generating two-dimensional sequences related to discrete approximations of irrational planes. These two-dimensional substitutions are produced by the classical Jacobi-Perron continued fraction algorithm, by the way of induction of a Z2-action by rotations on the circle. This gives a new geometric interpretation of the Jacobi-Perron algorithm, as a map operating on the parameter space of Z2-actions by rotations.



Last update : september 17, 2001, EL.