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1995 | 116 | 3 | 207-215
Tytuł artykułu

On the multiplicity function of ergodic group extensions, II

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For an arbitrary set $A ⊆ ℕ^+$ containing 1, an ergodic automorphism T whose set of essential values of the multiplicity function is equal to A is constructed. If A is additionally finite, T can be chosen to be an analytic diffeomorphism on a finite-dimensional torus.
Słowa kluczowe
Czasopismo
Rocznik
Tom
116
Numer
3
Strony
207-215
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-04-25
poprawiono
1995-03-31
Twórcy
  • Department of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  • Department of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [1] L. M. Abramov, Metric automorphisms with quasi-discrete spectrum, Izv. Akad. Nauk SSSR 26 (1962), 513-550 (in Russian).
  • [2] O. N. Ageev, Dynamical systems with a Lebesgue component of even multiplicity in the spectrum, Mat. Sb. 136 (178) (1988), 307-319 (in Russian).
  • [3] F. Blanchard and M. Lemańczyk, Measure preserving diffeomorphisms with an arbitrary spectral multiplicity, Topol. Methods Nonlinear Anal. 1 (1993), 275-294.
  • [4] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer, 1981.
  • [5] S. Ferenczi and J. Kwiatkowski, Rank and spectral multiplicity, Studia Math. 102 (1992), 121-144.
  • [6] S. Ferenczi, J. Kwiatkowski and C. Mauduit, Density theorem for (multiplicity, rank) pairs, J. Anal. Math., to appear.
  • [7] G. R. Goodson, On the spectral multiplicity of a class of finite rank transformations, Proc. Amer. Math. Soc. 93 (1985), 303-306.
  • [8] G. R. Goodson, J. Kwiatkowski, M. Lemańczyk and P. Liardet, On the multiplicity function of ergodic group extensions of rotations, Studia Math. 102 (1992), 157-174.
  • [9] G. R. Goodson and M. Lemańczyk, On the rank of a class of bijective substitutions, ibid. 96 (1990), 219-230.
  • [10] A. del Junco and D. Rudolph, Simple rigid rank-1, Ergodic Theory Dynam. Systems 7 (1987), 229-247.
  • [11] A. B. Katok, Constructions in ergodic theory, preprint.
  • [12] A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Uspekhi Mat. Nauk 22 (5) (1967), 81-106 (in Russian); English transl.: Russian Math. Surveys 15 (1967), 1-22.
  • [13] J. King, Joining-rank and the structure of finite rank mixing transformations, J. Anal. Math. 51 (1988), 182-227.
  • [14] J. Kwiatkowski and A. Sikorski, Spectral properties of G-symbolic Morse shifts, Bull. Soc. Math. France 115 (1987), 19-33.
  • [15] M. Lemańczyk, Toeplitz $Z_2$-extensions, Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), 1-43.
  • [16] J. Mathew and M. G. Nadkarni, A measure preserving transformation whose spectrum has Lebesgue component of multiplicity two, Bull. London Math. Soc. 16 (1984), 402-406.
  • [17] M. K. Mentzen, Some examples of automorphisms with rank r and simple spectrum, Bull. Polish Acad. Sci. 35 (1987), 417-424.
  • [18] V. I. Oseledec, The spectrum of ergodic automorphisms, Dokl. Akad. Nauk SSSR 168 (1966), 776-779 (in Russian).
  • [19] W. Parry, Topics in Ergodic Theory, Cambridge Univ. Press, 1981.
  • [20] M. Queffélec, Substitution Dynamical Systems - Spectral Analysis, Lecture Notes in Math. 1294, Springer 1987.
  • [21] E. A. Robinson, Ergodic measure preserving transformations with arbitrary finite spectral multiplicities, Invent. Math. 72 (1983), 299-314.
  • [22] E. A. Robinson, Transformations with highly nonhomogeneous spectrum of finite multiplicity, Israel J. Math. 56 (1986), 75-88.
  • [23] E. A. Robinson, Spectral multiplicity for non-abelian Morse sequences, in: Lecture Notes in Math. 1342, Springer, 1988, 645-652.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv116i3p207bwm
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