On colorations induced by discrete rotations

Abstract

We consider a non numerable family of colorations induced by discrete rotations. The symbolical dynamical system associated with the coloration is first explained. We introduce then a group that supports the dynamics of the system. The periodical cases are precised, they are induced by Pythagorean triples. Finally, a proof of the quasi-periodicity of the colorations, and a description of asymmetrical colorations conclude this paper. © Springer-Verlag Berlin Heidelberg 2003.