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1992 | 102 | 2 | 121-144
Tytuł artykułu

Rank and spectral multiplicity

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a dynamical system (X,T,μ), we investigate the connections between a metric invariant, the rank r(T), and a spectral invariant, the maximal multiplicity m(T). We build examples of systems for which the pair (m(T),r(T)) takes values (m,m) for any integer m ≥ 1 or (p-1, p) for any prime number p ≥ 3.
Słowa kluczowe
Czasopismo
Rocznik
Tom
102
Numer
2
Strony
121-144
Opis fizyczny
Daty
wydano
1992
otrzymano
1991-07-09
Twórcy
  • CNRS, URA 225, 163 Avenue de Luminy, F-13288 Marseille Cedex 9, France
  • Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [Age] O. N. Ageev, Dynamical systems with a Lebesgue component of even multiplicity in the spectrum, Mat. Sb. 136 (178) (1988), 307-319 (in Russian).
  • [Cha1] R. V. Chacon, A geometric construction of measure preserving transformations, in: Proc. Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. II, Part 2, Univ. of California Press, 1965, 335-360.
  • [Cha2] R. V. Chacon, Approximation and spectral multiplicity, in: Contributions to Ergodic Theory and Probability, Lecture Notes in Math. 160, Springer, 1970, 18-27.
  • [Fer1] S. Ferenczi, Systèmes localement de rang un, Ann. Inst. H. Poincaré Probab. Statist. 20 (1984), 35-51.
  • [Fer2] S. Ferenczi, Tiling and local rank properties of the Morse sequence, Theoret. Comput. Sci., to appear.
  • [GKLL] G. R. Goodson, J. Kwiatkowski, M. Lemańczyk and P. Liardet, On the multiplicity function of ergodic group extensions of rotations, this volume, 157-174.
  • [GoLe] G. R. Goodson and M. Lemańczyk, On the rank of a class of bijective substitutions, Studia Math. 96 (1990), 219-230.
  • [delJ] A. del Junco, A transformation with simple spectrum which is not rank one, Canad. J. Math. 29 (1977), 655-663.
  • [Kea1] M. Keane, Generalized Morse sequences, Z. Wahrsch. Verw. Gebiete 10 (1968), 335-353.
  • [Kea2] M. Keane, Strongly mixing g-measures, Invent. Math. 16 (1972), 309-353.
  • [Kwi] J. Kwiatkowski, Isomorphism of regular Morse dynamical systems, Studia Math. 72 (1982), 59-89.
  • [KwRo] J. Kwiatkowski and T. Rojek, A method of solving a cocycle functional equation and applications, ibid. 99 (1991), 69-86.
  • [KwSi] J. Kwiatkowski and A. Sikorski, Spectral properties of G-symbolic Morse shifts, Bull. Soc. Math. France 115 (1987), 19-33.
  • [Lem] M. Lemańczyk, Toeplitz Z₂-extensions, Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), 1-43.
  • [Mar1] J. C. Martin, Generalized Morse sequences on n symbols, Proc. Amer. Math. Soc. 54 (1976), 379-383.
  • [Mar2] J. C. Martin, The structure of generalized Morse minimal sets on n symbols, Trans. Amer. Math. Soc. 232 (1977), 343-355.
  • [MaNa] 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.
  • [Men1] M. Mentzen, Some examples of automorphisms with rank r and simple spectrum, Bull. Polish Acad. Sci. Math. 35 (1987), 417-424.
  • [Men2] M. Mentzen, Thesis, preprint no. 2/89, Nicholas Copernicus University, Toruń 1989.
  • [New] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 19 (1979), 129-136.
  • [ORW] D. S. Ornstein, D. J. Rudolph and B. Weiss, Equivalence of measure preserving transformations, Mem. Amer. Math. Soc. 262 (1982).
  • [Par] W. Parry, Compact abelian group extensions of discrete dynamical systems, Z. Wahrsch. Verw. Gebiete 13 (1969), 95-113.
  • [Que] M. Queffélec, Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Math. 1294, Springer, 1987.
  • [Rob1] E. A. Robinson, Ergodic measure preserving transformations with arbitrary finite spectral multiplicities, Invent. Math. 72 (1983), 299-314.
  • [Rob2] E. A. Robinson, Mixing and spectral multiplicity, Ergodic Theory Dynamical Systems 5 (1985), 617-624.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv102i2p121bwm
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