Ergodicité générique des billards polygonaux
Un exemple de semi-conjugaison entre un échange d'intervalles et une translation sur le tore
Sturm numbers and substitution invariance of 3iet words.
Représentation géométrique de suites de complexité
Complexité de suites engendrées par des récurrences unipotentes
Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles
Trajectories of rotations
Discrete planes, -actions, Jacobi-Perron 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 -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 -actions by rotations.
Complexity of sequences defined by billiard in the cube
Fractal representation of the attractive lamination of an automorphism of the free group
In this paper, we extend to automorphisms of free groups some results and constructions that classically hold for morphisms of the free monoid, i.e., the so-called substitutions. A geometric representation of the attractive lamination of a class of automorphisms of the free group (irreducible with irreducible powers () automorphisms) is given in the case where the dilation coefficient of the automorphism is a unit Pisot number. The shift map associated with the attractive symbolic lamination is,...
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