Dynamical Systems
S-adic conjecture and Bratteli diagrams
[Conjecture S-adique et les représentations de Bratteli]
Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 979-983.

Dans cette Note nous utilisons une amélioration conséquente dʼun résultat de S. Ferenczi, concernant les sous-shifts S-adiques, afin dʼen trouver des représentations de Bratteli–Vershik.

In this Note we apply a substantial improvement of a result of S. Ferenczi on S-adic subshifts to give Bratteli–Vershik representations of these subshifts.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.10.015
Durand, Fabien 1 ; Leroy, Julien 1

1 Université de Picardie Jules-Verne, laboratoire amiénois de mathématiques fondamentales et appliquées, CNRS-UMR 7352, 33, rue Saint Leu, 80039 Amiens cedex, France
@article{CRMATH_2012__350_21-22_979_0,
     author = {Durand, Fabien and Leroy, Julien},
     title = {\protect\emph{S}-adic conjecture and {Bratteli} diagrams},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {979--983},
     publisher = {Elsevier},
     volume = {350},
     number = {21-22},
     year = {2012},
     doi = {10.1016/j.crma.2012.10.015},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2012.10.015/}
}
TY  - JOUR
AU  - Durand, Fabien
AU  - Leroy, Julien
TI  - S-adic conjecture and Bratteli diagrams
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 979
EP  - 983
VL  - 350
IS  - 21-22
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2012.10.015/
DO  - 10.1016/j.crma.2012.10.015
LA  - en
ID  - CRMATH_2012__350_21-22_979_0
ER  - 
%0 Journal Article
%A Durand, Fabien
%A Leroy, Julien
%T S-adic conjecture and Bratteli diagrams
%J Comptes Rendus. Mathématique
%D 2012
%P 979-983
%V 350
%N 21-22
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2012.10.015/
%R 10.1016/j.crma.2012.10.015
%G en
%F CRMATH_2012__350_21-22_979_0
Durand, Fabien; Leroy, Julien. S-adic conjecture and Bratteli diagrams. Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 979-983. doi : 10.1016/j.crma.2012.10.015. http://www.numdam.org/articles/10.1016/j.crma.2012.10.015/

[1] Arnoux, P.; Rauzy, G. Représentation géométrique de suites de complexité 2n+1, Bull. Soc. Math. France, Volume 119 (1991), pp. 199-215

[2] Cassaigne, J. Special factors of sequences with linear subword complexity, Magdeburd, 1995, World Sci. Publ., River Ege, NJ (1996), pp. 25-34

[3] Downarowicz, T.; Maass, A. Finite rank Bratteli–Vershik diagrams are expansive, Ergod. Theory Dynam. Sys., Volume 28 (2008), pp. 739-747

[4] Durand, F. Combinatorics on Bratteli diagrams and dynamical systems, Combinatorics, Automata and Number Theory, Series Encyclopedia of Mathematics and Its Applications, vol. 135, Cambridge University Press, 2010, pp. 338-386

[5] Durand, F.; Host, B.; Skau, C. Substitutive dynamical systems, Bratteli diagrams and dimension groups, Ergod. Theory Dynam. Sys., Volume 19 (1999), pp. 953-993

[6] Ferenczi, S. Rank and symbolic complexity, Ergod. Theory Dynam. Sys., Volume 16 (1996), pp. 663-682

[7] Giordano, T.; Putnam, I.; Skau, C. Topological orbit equivalence and C-crossed products, Internat. J. Math., Volume 469 (1995), pp. 51-111

[8] Herman, R.H.; Putnam, I.; Skau, C.F. Ordered Bratteli diagrams, dimension groups and topological dynamics, Internat. J. Math., Volume 3 (1992), pp. 827-864

[9] J. Leroy, Contribution à la résolution de la conjecture S-adique, PhD thesis, Univ. Picardie Jules Verne, 2011.

[10] Leroy, J. Some improvements of the S-adic conjecture, Adv. Appl. Math., Volume 48 (2012), pp. 79-98

[11] J. Leroy, G. Richomme, A combinatorial proof of S-adicity for sequences with sub-affine complexity, preprint.

[12] Morse, M.; Hedlund, G.A. Symbolic dynamics, Amer. J. Math., Volume 60 (1938), pp. 815-866

[13] Morse, M.; Hedlund, G.A. Symbolic dynamics II. Sturmian trajectories, Amer. J. Math., Volume 62 (1940), pp. 1-42

[14] Queffélec, M. Substitution Dynamical Systems – Spectral Analysis, Lecture Notes in Mathematics, vol. 1294, Springer-Verlag, Berlin, 1987

[15] Vershik, A.M. A theorem on the Markov periodical approximation in ergodic theory, J. Sov. Math., Volume 28 (1985), pp. 667-674

Cité par Sources :