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.
@article{bwmeta1.element.bwnjournal-article-cmv84i2p285bwm,
author = {Guy Barat and Tomasz Downarowicz and Anzelm Iwanik and Pierre Liardet},
title = {Propri\'et\'es topologiques et combinatoires des \'echelles de num\'eration},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {285-306},
zbl = {1001.54026},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv84i2p285bwm}
}
Barat, Guy; Downarowicz, Tomasz; Iwanik, Anzelm; Liardet, Pierre. Propriétés topologiques et combinatoires des échelles de numération. Colloquium Mathematicae, Tome 84/85 (2000) pp. 285-306. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv84i2p285bwm/
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