Les transformations de Chacon : combinatoire, structure géométrique, lien avec les systèmes de complexité 2 n + 1

Sébastien Ferenczi

Bulletin de la Société Mathématique de France (1995)

  • Volume: 123, Issue: 2, page 271-292
  • ISSN: 0037-9484

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Ferenczi, Sébastien. "Les transformations de Chacon : combinatoire, structure géométrique, lien avec les systèmes de complexité $2n+1$." Bulletin de la Société Mathématique de France 123.2 (1995): 271-292. <http://eudml.org/doc/87718>.

@article{Ferenczi1995,
author = {Ferenczi, Sébastien},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Chacon's map; complexity; transformation; weakly mixing systems},
language = {fre},
number = {2},
pages = {271-292},
publisher = {Société mathématique de France},
title = {Les transformations de Chacon : combinatoire, structure géométrique, lien avec les systèmes de complexité $2n+1$},
url = {http://eudml.org/doc/87718},
volume = {123},
year = {1995},
}

TY - JOUR
AU - Ferenczi, Sébastien
TI - Les transformations de Chacon : combinatoire, structure géométrique, lien avec les systèmes de complexité $2n+1$
JO - Bulletin de la Société Mathématique de France
PY - 1995
PB - Société mathématique de France
VL - 123
IS - 2
SP - 271
EP - 292
LA - fre
KW - Chacon's map; complexity; transformation; weakly mixing systems
UR - http://eudml.org/doc/87718
ER -

References

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  1. [1] ARNOUX (P.) et RAUZY (G.). — Représentation géométrique de suites de complexité 2n + 1, Bull. Soc. Math. France., t. 119, 1991, p. 199-215. Zbl0789.28011MR92k:58072
  2. [2] CHACON (R.V.). — Weakly mixing transformations which are not strongly mixing, Proc. Amer. Math. Soc., t. 22, 1969, p. 559-562. Zbl0186.37203MR40 #297
  3. [3] DEKKING (F.M.). — The spectrum of dynamical systems arising from substitutions of constant length, Zeit. Wahr., t. 41, 1978, p. 221-239. Zbl0348.54034MR57 #1455
  4. [4] DEL JUNCO (A.), RAHE (A. M.) and SWANSON (M.). — Chacon's automorphism has minimal self-joinings, J. Analyse Math., t. 37, 1980, p. 276-284. Zbl0445.28014MR81j:28027
  5. [5] DEL JUNCO (A.) and RUDOLPH (D.J.). — A rank-one, rigid, simple, prime map, Ergodic Th. Dyn. Syst. 7, t. 2, 1987, p. 229-247. Zbl0634.54020MR88h:28016
  6. [6] FERENCZI (S.). — Systèmes de rang fini, Thèse d'Etat, Université d'Aix-Marseille 2, 1990. 
  7. [7] FIELDSTEEL (A.). — An uncountable family of prime transformations not isomorphic to their inverses, preprint, vers 1980. 
  8. [8] HERMAN (R.H.), PUTNAM (I.F.) and SKAU (C.F.). — Ordered Bratteli diagrams, dimension groups and topological dynamics, International J. of Maths 3, t. 6, 1992, p. 827-864. Zbl0786.46053MR94f:46096
  9. [9] HOST (B.). — Dimension groups and substitution dynamical systems, Prétirage du Laboratoire de Mathématiques Discrètes, 1994. 
  10. [10] MOSSE (B.). — Notions de reconnaissabilité pour les substitutions et complexité des suites automatiques, soumis. 
  11. [11] ORNSTEIN (D.S.). — On the root problem in ergodic theory, Proc. of the Sixth Berkeley Symposium in Mathematical Statistics and Probability, Univ. of California Press, 1970, p. 347-356. Zbl0262.28009MR53 #3259

Citations in EuDML Documents

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  1. Izumi Nakashima, Jun-Ichi Tamura, Shin-Ichi Yasutomi, *-sturmian words and complexity
  2. Charles Holton, Luca Q. Zamboni, Geometric realizations of substitutions
  3. Rebecca Risley, Luca Zamboni, A generalization of Sturmian sequences: Combinatorial structure and transcendence
  4. Julien Cassaigne, Sébastien Ferenczi, Luca Q. Zamboni, Imbalances in Arnoux-Rauzy sequences
  5. L'ubomíra Balková, Edita Pelantová, Štěpán Starosta, Sturmian jungle (or garden?) on multiliteral alphabets
  6. L'ubomíra Balková, Edita Pelantová, Štěpán Starosta, Sturmian jungle (or garden?) on multiliteral alphabets
  7. Sébastien Ferenczi, Systems of finite rank

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