Comptes Rendus
Dynamical Systems
S-adic conjecture and Bratteli diagrams
[Conjecture S-adique et les représentations de Bratteli]
Comptes Rendus. Mathématique, Volume 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

Fabien Durand 1 ; Julien Leroy 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
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Fabien Durand; Julien Leroy. S-adic conjecture and Bratteli diagrams. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 979-983. doi : 10.1016/j.crma.2012.10.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.015/

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

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

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

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

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

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

[8] R.H. Herman; I. Putnam; C.F. Skau 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] J. Leroy 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] M. Morse; G.A. Hedlund Symbolic dynamics, Amer. J. Math., Volume 60 (1938), pp. 815-866

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

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

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

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