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ArticleOriginal scientific text

Title

Propriétés topologiques et combinatoires des échelles de numération

Authors 1, 2, , 3

Affiliations

  1. 20, rue Fourcroy, F-75017 Paris
  2. Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
  3. Université de Provence, Centre de Mathématiques et Informatique, 39, rue Joliot-Curie, F-13453 Marseille Cedex 13

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.

Keywords

ENG
dynamical system, addingi machine, odometer, rooted tree, number system

Bibliography

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Colloquium Mathematicum
2000/84/85/2
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Pages:
285-306
Main language of publication
French
Received
1999-08-02
Accepted
1999-12-03
Published
2000
Exact and natural sciences