Propriétés topologiques et combinatoires des échelles de numération
Volume 84 / 2000
Colloquium Mathematicum 84 (2000), 285-306
DOI: 10.4064/cm-84/85-2-285-306
Abstract
Topological and combinatorial properties of dynamical systems called odometers and arising from number systems are investigated. First, a topological classification is obtained. Then a rooted tree describing the carries in the addition of 1 is introduced and extensively studied. It yields a description of points of discontinuity and a notion of low scale, which is helpful in producing examples of what the dynamics of an odometer can look like. Density of the orbits is also discussed.
