Propriétés topologiques et combinatoires des échelles de numération

Volume 84 / 2000

Guy Barat, Tomasz Downarowicz, Anzelm Iwanik, Pierre Liardet Colloquium Mathematicum 84 (2000), 285-306 DOI: 10.4064/cm-84/85-2-285-306


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.


  • Guy Barat
  • Tomasz Downarowicz
  • Anzelm Iwanik
  • Pierre Liardet

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