Discrete planes, ℤ 2 -actions, Jacobi-Perron algorithm and substitutions
Pierre Arnoux, Valérie Berthé, Shunji Ito · Annales de l’institut Fourier · 2002
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 ℤ 2 -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 ℤ 2 -actions by rotations.