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1994-1995 | 112 | 2 | 141-164
Tytuł artykułu

Semisimplicity, joinings and group extensions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a theory of self-joinings for semisimple maps and their group extensions which is a unification of the following three cases studied so far: (iii) Gaussian-Kronecker automorphisms: [Th], [Ju-Th]. (ii) MSJ and simple automorphisms: [Ru], [Ve], [Ju-Ru]. (iii) Group extension of discrete spectrum automorphisms: [Le-Me], [Le], [Me].
Słowa kluczowe
Czasopismo
Rocznik
Tom
112
Numer
2
Strony
141-164
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-12-06
poprawiono
1994-04-04
Twórcy
autor
  • Department of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland, mlem@mat.uni.torun.pl
autor
  • Department of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland, mentzen@mat.uni.torun.pl
Bibliografia
  • [An] H. Anzai, Ergodic skew product transformations on the torus, Osaka J. Math. 3 (1951), 83-99.
  • [Fi-Ru] A. Fieldsteel and D. Rudolph, An ergodic transformation with trivial Kakutani centralizer, Ergodic Theory Dynamical Systems 12 (1992), 459-478.
  • [Fu] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, Princeton, N.J., 1981.
  • [Gl-Ho-Ru] E. Glasner, B. Host and D. Rudolph, Simple systems and their higher order self-joinings, Israel J. Math. 78 (1992), 131-142.
  • [Ju-Ru] A. del Junco and D. Rudolph, On ergodic actions whose self-joinings are graphs, Ergodic Theory Dynamical Systems 7 (1987), 531-557.
  • [Ju-Th] A. del Junco and J.-P. Thouvenot, The theory for Gaussian-Kronecker automorphisms, preprint.
  • [Ke-Ne1] H. B. Keynes and D. Newton, Choquet Theory and Ergodic Measures for Compact Group Extensions, Lecture Notes in Math. 318, Springer, 1973.
  • [Ke-Ne2] H. B. Keynes and D. Newton, The structure of ergodic measures for compact group extensions, Israel J. Math. 18 (1974), 363-389.
  • [Ke-Ne3] H. B. Keynes and D. Newton, Ergodic measures for nonabelian compact group extensions, Compositio Math. 32 (1976), 53-70.
  • [Le] M. Lemańczyk, Ergodic abelian group extensions of rotations, preprint, Toruń 1990.
  • [Le] M. Lemańczyk and M. K. Mentzen, Compact subgroups in the centralizer of natural factors of an ergodic group extension of a rotation determine all factors, Ergodic Theory Dynamical Systems 10 (1990), 763-776.
  • [Me] M. K. Mentzen, Ergodic properties of group extensions of dynamical systems with discrete spectra, Studia Math. 101 (1991), 19-31.
  • [Ne] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 19 (1979), 129-136.
  • [Ne1] D. Newton, Coalescence and spectrum of automorphisms of a Lebesgue space, Z. Wahrsch. Verw. Gebiete 19 (1971), 117-122.
  • [Ru] D. Rudolph, An example of measure preserving map with minimal self-joinings, and applications, J. Analyse Math. 35 (1979), 97-122.
  • [Ru1] D. Rudolph, Classifying the isometric extensions of a Bernoulli shift, ibid. 34 (1978), 36-60.
  • [Th] J.-P. Thouvenot, The metrical structure of some Gaussian processes, in: Proc. Ergodic Theory and Related Topics II, Georgenthal 1986, 195-198.
  • [Ve] W. A. Veech, A criterion for a process to be prime, Monatsh. Math. 94 (1982), 335-341.
  • [Zi] R. Zimmer, Extensions of ergodic group actions, Illinois J. Math. 20 (1976), 373-409.
  • [Zi1] R. Zimmer, Ergodic actions with generalized discrete spectrum, ibid., 555-588.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv112i2p141bwm
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