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2000 | 142 | 1 | 25-45
Tytuł artykułu

Orbit equivalence and Kakutani equivalence with Sturmian subshifts

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Using dimension group tools and Bratteli-Vershik representations of minimal Cantor systems we prove that a minimal Cantor system and a Sturmian subshift are topologically conjugate if and only if they are orbit equivalent and Kakutani equivalent.
Czasopismo
Rocznik
Tom
142
Numer
1
Strony
25-45
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-06-28
Twórcy
autor
  • Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile
autor
  • Faculté de Mathématiques et d'Informatique, Université de Picardie Jules Verne, 33 rue Saint Leu, 80000 Amiens, France
autor
  • Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile
Bibliografia
  • [BS] J. Berstel et P. Séébold, Morphismes de Sturm, Bull. Belg. Math. Soc. 1 (1994), 175-189.
  • [BH] M. Boyle and D. Handelmann, Orbit equivalence and ordered cohomology, Israel J. Math. 95 (1996), 169-210.
  • [BT] M. Boyle and J. Tomiyama, Bounded topological equivalence and C*-algebras, J. Math. Soc. Japan 50 (1998), 317-329.
  • [D] F. Durand, Contributions à l'étude des suites et systèmes dynamiques substitutifs, thèse de doctorat, Université d'Aix-Marseille II, 1996.
  • [DHS] F. Durand, B. Host and C. F. Skau, Substitutional dynamical systems, Bratteli diagrams and dimension groups, Ergodic Theory Dynam. Systems 19 (1999), 953-993.
  • [ES] E. G. Effros and C.-L. Shen, Approximately finite C*-algebras and continued fractions, Indiana Univ. Math. J. 29 (1980), 191-204.
  • [F] A. H. Forrest, K-groups associated with substitution minimal systems, Israel J. of Math. 98 (1997), 101-139.
  • [GPS] T. Giordano, I. Putnam and C. F. Skau, Topological orbit equivalence and C*-crossed products, J. Reine Angew. Math. 469 (1995), 51-111.
  • [GJ] R. Gjerde and O. Johansen, Bratteli-Vershik models for Cantor minimal systems: applications to Toeplitz flows, Ergodic Theory Dynam. Systems, to appear.
  • [HW] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed.. Oxford, 1975.
  • [HM] G. A. Hedlund and M. Morse, Symbolic dynamics II. Sturmian trajectories, Amer. J. Math. 62 (1940), 1-42.
  • [HPS] R. H. Herman, I. Putnam and C. F. Skau, Ordered Bratteli diagrams, dimension groups and topological dynamics, Internat. J. Math. 3 (1992), 827-864.
  • [H] B. Host, Dimension groups and substitution dynamical systems, preprint 13, Inst. Math. de Luminy, 1995.
  • [K] H. Kesten, On a conjecture of Erdös and Szüsz related to uniform distribution mod 1, Acta Arithmetica 12 (1966), 193-212.
  • [MS] F. Mignosi et P. Séébold, Morphismes sturmiens et règles de Rauzy, J. Théorie Nombres Bordeaux 5 (1993), 221-233.
  • [O] N. Ormes, Strong orbit realizations for minimal homeomorphisms, J. Anal. Math. 71 (1997), 103-133.
  • [P] B. Parvaix, Substitution invariant Sturmian bisequences, J. Théorie Nombres Bordeaux 11 (1999), 201-210.
  • [Q] M. Queffélec, Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Math. 1294, Springer, 1988.
  • [S] C.-L. Shen, A note on the automorphism groups of simple dimension groups, Pacific J. Math. 89 (1980), 199-207.
  • [Su] F. Sugisaki, The relationship between entropy and strong orbit equivalence for the minimal homeomorphisms. II, Tokyo J. Math. 21 (1998), 311-351.
  • [V1] A. M. Vershik, A theorem on the Markov periodic approximation in ergodic theory, J. Soviet Math. 28 (1985), 667-674.
  • [V2] A. M. Vershik, Uniform algebraic approximation of shift and multiplication operators, Soviet Math. Dokl. 24 (1981), 97-100.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv142i1p25bwm
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