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2000 | 84/85 | 1 | 203-227
Tytuł artykułu

Ordered K-theoryand minimal symbolic dynamical systems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Recently a new invariant of K-theoretic nature has emerged which is potentially very useful for the study of symbolic systems. We give an outline of the theory behind this invariant. Then we demonstrate the relevance and power of the invariant, focusing on the families of substitution minimal systems and Toeplitz flows.
Słowa kluczowe
Rocznik
Tom
Numer
1
Strony
203-227
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-07-14
poprawiono
1999-11-15
Twórcy
  • Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Bibliografia
  • [1] M. Boyle, Topological orbit equivanlence and factor maps in symbolic dynamics, Ph.D. thesis, Univ. of Washington, 1983.
  • [2] O. Bratteli, Inductive limits of finite dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234.
  • [3] T. Downarowicz, The Choquet simplex of invariant measures for minimal flows, Israel J. Math. 74 (1991), 241-256.
  • [4] T. Downarowicz and F. Durand, Factors of Toeplitz flows and other almost 1-1 extensions over group rotations, preprint, 1998.
  • [5] T. Downarowicz and Y. Lacroix, Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows, Studia Math. 130 (1998), 149-170.
  • [6] F. Durand, B. Host and C. Skau, Substitution dynamical systems, Bratteli diagrams, and dimension groups, Ergodic Theory Dynam. Systems, to appear.
  • [7] E. G. Effros, Dimensions and C*-algebras, CBMS Regional Conf. Ser. in Math. 46, Conf. Board Math. Sci. and Amer. Math. Soc., 1981.
  • [8] E. Effros, D. Handelman and C.-L. Shen, Dimension groups and their affine reprensentations, Amer. J. Math. 102 (1980), 385-407.
  • [9] G. A. Elliott, On the classification of inductive limits of sequences of semisimple finite dimensional algebras, J. Algebra 38 (1976), 29-44.
  • [10] A. H. Forrest, K-groups associated with substitution minimal systems, Israel J. Math. 98 (1997), 101-139.
  • [11] T. Giordano, I. F. Putnam and C. F. Skau, Topological orbit equivalence and C*-crossed products, J. Reine Angew. Math. 469 (1995), 51-111.
  • [12] R. Gjerde and O. Johansen, Bratteli-Vershik models for Cantor minimal systems: Applications to Toeplitz flows, NB Ergodic Theory Dynam. Systems, to appear.
  • [13] E. Glasner and B. Weiss, Weak orbit equivalence of Cantor minimal systems, Internat. J. Math. 6 (1995), 569-579.
  • [14] D. Handelman, Positive matrices and dimension groups affiliated to topological Markov chains, in: Proc. Sympos. Pure Math. 38, part I, Amer. Math. Soc., 1982, 191-194.
  • [15] T. Harju and M. Linna, On the periodicity of morphisms on free monoids, RAIRO Inform. Théor. Appl. 20 (1986), 47-54.
  • [16] R. H. Herman, I. F. Putnam and C. F. Skau, Ordered Bratteli diagrams, dimension groups, and topological dynamics, Internat. J. Math. 3 (1992), 827-864.
  • [17] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis I, Grundlehren Math. Wiss. 115, Springer, Berlin, 1963.
  • [18] B. Mossé, Puissances de mots et reconnaissabilité des points fixes d'une substitution, Theoret. Comput. Sci. 99 (1992), 327-334.
  • [19] --, Reconnaissabilité des substitutions et complexité des suites automatiques, Bull. Soc. Math. France 124 (1996), 101-118.
  • [20] N. Ormes, Strong orbit realization for minimal homeomorphisms, J. Anal. Math. 71 (1997), 103-133.
  • [21] W. Parry and S. Tuncel, Classification Problems in Ergodic Theory, London Math. Soc. Lecture Note Ser. 67, Cambridge Univ. Press, Cambridge, 1982.
  • [22] I. F. Putnam, K. Schmidt and C. Skau, C*-algebras associated with Denjoy homeomorphisms of the circle, J. Operator Theory 16 (1986), 99-126.
  • [23] M. Queffélec, Substitution Dynamical Systems, Lecture Notes in Math. 1294, Springer, (1987).
  • [24] F. Sugisaki, The relationship between entropy and strong orbit equivalence for the minimal homeomorphisms (I), Internat. J. Math., to appear.
  • [25] A. M. Vershik, A theorem on the Markov periodical approximation in ergodic theory, J. Soviet Math. 28 (1985), 667-674.
  • [26] P. Walters, An Introduction to Ergodic Theory, Grad. Texts in Math. 79, Springer, 1982.
  • [27] S. Williams, Toeplitz minimal flows which are not uniquely ergodic, Z. Wahrsch. Verw. Gebiete 67 (1984), 95-107.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv84i1p203bwm
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