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1998 | 130 | 2 | 149-170
Tytuł artykułu

Almost 1-1 extensions of Furstenberg-Weiss type and applications to Toeplitz flows

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let $(Z,T_Z)$ be a minimal non-periodic flow which is either symbolic or strictly ergodic. Any topological extension of $(Z,T_Z)$ is Borel isomorphic to an almost 1-1 extension of $(Z,T_Z)$. Moreover, this isomorphism preserves the affine-topological structure of the invariant measures. The above extends a theorem of Furstenberg-Weiss (1989). As an application we prove that any measure-preserving transformation which admits infinitely many rational eigenvalues is measure-theoretically isomorphic to a strictly ergodic toeplitz flow.
Czasopismo
Rocznik
Tom
130
Numer
2
Strony
149-170
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-04-06
poprawiono
1997-11-19
Twórcy
autor
Y.
  • Département de Mathématiques, Faculté des Sciences, Université de Bretagne Occidentale, 6 Avenue V. Le Gorgeu, B.P. 809, 29285 Brest Cedex, France , lacroix@univ-brest.fr
Bibliografia
  • [A] J. Auslander, Minimal Flows and Their Extensions, North-Holland Math. Stud. 153, North-Holland, 1988.
  • [B-G-K] F. Blanchard, E. Glasner and J. Kwiatkowski, Minimal self-joinings and positive topological entropy, Monatsh. Math. 120 (1995), 205-222.
  • [B-K1] W. Bułatek and J. Kwiatkowski, The topological centralizers of Toeplitz flows and their $Z_2$ -extensions, Publ. Math. 34 (1990), 45-65.
  • [B-K2] W. Bułatek and J. Kwiatkowski, Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers, Studia Math. 103 (1992), 133-142.
  • [D-G-S] M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, Berlin, 1976.
  • [D-K] M. Denker and M. Keane, Almost topological dynamical systems, Israel J. Math. 34 (1979), 139-160.
  • [D1] T. Downarowicz, A minimal 0-1 subshift with noncompact set of invariant measures, Probab. Theory Related Fields 79 (1988), 29-35
  • [D2] T. Downarowicz, The Choquet simplex of invariant measures for minimal flows, Israel J. Math. 74 (1991), 241-256.
  • [D3] T. Downarowicz, The Royal Couple conceals their mutual relationship - A noncoalescent Toeplitz flow, ibid. 97 (1997), 239-252.
  • [D-1] T. Downarowicz and A. Iwanik, Quasi-uniform convergence in compact dynamical systems, Studia Math. 89 (1998), 11-25.
  • [D-K-L] T. Downarowicz, J. Kwiatkowski and Y. Lacroix, A criterion for Toeplitz flows to be topologically isomorphic and applications, Colloq. Math. 68 (1995), 219-228.
  • [D-L] T. Downarowicz and Y. Lacroix, A non-regular Toeplitz flow with preset pure point spectrum, Studia Math. 120 (1996), 235-246.
  • [E] E. Eberlein, Toeplitzfolgen und Gruppentranslationen, Thesis, Erlangen, 1970.
  • [F-K-M] S. Férenczi, J. Kwiatkowski and C. Mauduit, A density theorem for (multiplicity, rank) pairs, J. Anal. Math. 65 (1995), 45-75.
  • [F-W] H. Furstenberg and B. Weiss, On almost 1-1 extensions, Israel J. Math. 65 (1989), 311-322.
  • [Ga-H] M. Garsia and G. A. Hedlund, The structure of minimal sets, Bull. Amer. Math. Soc. 54 (1948), 954-964.
  • [G-H] W. H. Gottschalk and G. A. Hedlund, Topological Dynamics, Amer. Math. Soc. Colloq. Publ. 36, 1995.
  • [H-R] E. Hewitt and K. Ross, Abstract Harmonic Analysis, Vol. I, Springer, Berlin, 1963.
  • [I] A. Iwanik, Toeplitz flows with pure point spectrum, Studia Math. 118 (1996), 27-35.
  • [I-L] A. Iwanik and Y. Lacroix, Some constructions of strictly ergodic non-regular Toeplitz flows, ibid. 110 (1994), 191-203
  • [J-K] K. Jacobs and M. Keane, 0-1 sequences of Toeplitz type, Z. Wahrsch. Verw. Gebiete 13 (1969), 123-131.
  • [K-L] J. Kwiatkowski and Y. Lacroix, Rank and weak closure theorem, II, preprint.
  • [L] M. Lemańczyk, Toeplitz $Z_2$-extensions, Ann. Inst. H. Poincaré 24 (1998), 1-43.
  • [M-P] N. Markley and M. E. Paul, Almost automorphic symbolic minimal sets without unique ergodicity, Israel J. Math. 34 (1979), 259-272.
  • [O] J. C. Oxtoby, Ergodic sets, Bull. Amer. Math. Soc. 58 (1952), 116-136.
  • [W] B. Weiss, Strictly ergodic models for dynamical systems, ibid. 13 (1985), 143-146.
  • [Wi] 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-smv130i2p149bwm
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