Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
285-306
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-08-02
poprawiono
1999-12-03
Twórcy
autor
- 20, rue Fourcroy, F-75017 Paris
autor
- Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
autor
autor
- Université de Provence, Centre de Mathématiques et Informatique, 39, rue Joliot-Curie, F-13453 Marseille Cedex 13
Bibliografia
- [Ba] G. Barat, Échelles de numération et fonctions arithmétiques associées, Thèse de doctorat, Université de Provence, Marseille, 1995.
- [BaDoLi] G. Barat, T. Downarowicz et P. Liardet, Dynamiques associées à une échelle de numération, preprint.
- [BeSh] R. Belleman and H. N. Shapiro, On a problem in additive number theory, Ann. of Math. 49 (1948), 333-340.
- [Be] J. Bésineau, Indépendance statistique d'ensembles liés à la fonction 'somme des chiffres', Acta Arith. 20 (1972), 401-416.
- [Br] Bratteli O. Bratteli, Inductive limits of finite dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234.
- [BrKrStP] H. Bruin, G. Keller and M. St. Pierre, Adding machines and wild attractors, Ergodic Theory Dynam. Systems 17 (1997), 1267-1287.
- [Co1] J. Coquet, Contribution à l'étude harmonique de suites arithmétiques, Thèse d'État, Univ. Paris-Sud, Orsay, 1978.
- [Do] M. Doudekova, Contribution à l'étude dynamique de translations par intervalles, Thèse de l'Université de Provence, Marseille, 1999.
- [DrGa] M. Drmota and J. Gajdosik, The distribution of the sum-of-digits function, J. Théor. Nombres Bordeaux 10 (1998), 17-32.
- [Fra]Fraenkel A. S. Fraenkel, Systems of numeration, Amer. Math. Monthly 92 (1985), 105-114.
- [Fro] C. Frougny, On the sequentiality of the successor function, Inform. and Comput. 139 (1997), 17-37.
- [GrLiTi] P. J. Grabner, P. Liardet and R. F. Tichy, Odometers and systems of numeration, Acta Arith. 70 (1995), 103-123.
- [HePuSk] R. H. Herman, I. F. Putman and C. F. Skau, Ordered Bratteli diagrams dimension groups and topological dynamics, Internat. J. Math. 3 (1992), 827-864.
- [Li1] P. Liardet, Propriétés harmoniques de la numération suivant Jean Coquet, Publ. Math. d'Orsay, no. 88-02, Colloque de Théorie des Nombres 'Jean Coquet', 1988, 1-35.
- [Li2] P. Liardet, Some group extensions over generalized odometers, International Conference on Ergodic Theory, Szklarska Poręba, June 19-25, 1989 (non publié).
- [Li3] P. Liardet, Some ergodic transformations arising from numerations in number fields, Ergodic Theory and Dynamical Systems, Conference held in Szklarska Poręba, September 7-13, 1997 (non publié).
- [Ma] J.-L. Mauclaire, An almost-sure estimate for the mean of generalized Q-multiplicative functions of modulus 1, J. Théor. Nombres Bordeaux, 1999, à paraître.
- [Os] A. Ostrowski, Bemerkungen zur Theorie des diophantischen Approximationen I, II, Abh. Math. Sem. Hamburg 1 (1922), 77-98, 250-251.
- [Pa] W. Parry, On the β-expansions of the real numbers, Acta Math. Acad. Sci. Hungar. 11 (1960), 401-416.
- [SiVe] N. A. Sidorov and A. M. Vershik, Arithmetic expansions associated with a rotation on the circle and with continued fractions, St Petersburg Math. J. 5 (1994), 1121-1136.
- [Ve] A. M. Vershik, Uniform algebraic approximation of shift and multiplication operators, Dokl. Akad. Nauk SSSR 259 (1981), 526-529 (in Russian); English transl.: Soviet Math. Dokl. 24 (1981), 97-100.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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