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1992 | 102 | 2 | 157-174
Tytuł artykułu

On the multiplicity function of ergodic group extensions of rotations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For an arbitrary set A ⊆ ℕ satisfying 1 ∈ A and lcm(m₁,m₂) ∈ A whenever m₁,m₂ ∈ A, an ergodic abelian group extension of a rotation for which the range of the multiplicity function equals A is constructed.
Słowa kluczowe
Czasopismo
Rocznik
Tom
102
Numer
2
Strony
157-174
Opis fizyczny
Daty
wydano
1992
otrzymano
1991-08-08
Twórcy
  • Mathematics Department, Towson State University, Towson, Maryland 21204-7097, U.S.A.
  • Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  • Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
autor
  • Université de Provence, Unité de Recherche Associée CNRS No. 225, Case 96, 3 Place Victor Hugo, 13331 Marseille Cedex 3, France
Bibliografia
  • [1] O. N. Ageev, Dynamical systems with a Lebesgue component of even multiplicity in the spectrum, Mat. Sb. 136 (178) (1988), 307-319 (in Russian).
  • [2] S. Ferenczi and J. Kwiatkowski, Rank and spectral multiplicity function, this volume, 201-224.
  • [3] G. R. Goodson, On the spectral multiplicity of a class of finite rank transformations, Proc. Amer. Math. Soc. 93 (1985), 303-306.
  • [4] G. R. Goodson and M. Lemańczyk, On the rank of a class of bijective substitutions, Studia Math. 96 (1990), 219-230.
  • [5] A. B. Katok, Constructions in Ergodic Theory, Progr. Math., Birkhäuser, Boston, Mass., to appear.
  • [6] M. Keane, Generalized Morse sequences, Z. Wahrsch. Verw. Gebiete 10 (1968), 335-353.
  • [7] J. Kwiatkowski, Spectral isomorphism of Morse dynamical systems, Bull. Acad. Polon. Sci. 29 (1981), 105-114.
  • [8] J. Kwiatkowski and A. Sikorski, Spectral properties of G-symbolic Morse shifts, Bull. Soc. Math. France 115 (1987), 19-33.
  • [9] M. Lemańczyk, Toeplitz Z₂-extensions, Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), 1-43.
  • [10] J. C. Martin, Generalized Morse sequences on n symbols, Proc. Amer. Math. Soc. 54 (1976), 379-383.
  • [11] J. C. Martin, The structure of generalized Morse minimal sets on n symbols, Trans. Amer. Math. Soc. 232 (1977), 343-355.
  • [12] J. Mathew and M. G. Nadkarni, Measure preserving transformations whose spectra have a Lebesgue component of finite multiplicity, preprint.
  • [13] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 19 (1979), 129-136.
  • [14] W. Parry, Compact abelian group extensions of discrete dynamical systems, Z. Wahrsch. Verw. Gebiete 13 (1969), 95-113.
  • [15] M. Queffélec, Contribution à l'étude spectrale de suites arithmétiques, Thèse, 1984.
  • [16] E. A. Robinson, Ergodic measure preserving transformations with arbitrary finite spectral multiplicities, Invent. Math. 72 (1983), 299-314.
  • [17] E. A. Robinson, Transformations with highly nonhomogeneous spectrum of finite multiplicity, Israel J. Math. 56 (1986), 75-88.
  • [18] E. A. Robinson, Spectral multiplicity for non-abelian Morse sequences, in: Lecture Notes in Math. 1342, Springer, 1988, 645-652.
  • [19] E. A. Robinson, Non-abelian extensions have nonsimple spectra, Compositio Math. 65 (1988), 155-170.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv102i2p157bwm
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