de Mathématiques de Luminy
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.