PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1999 | 133 | 3 | 249-256
Tytuł artykułu

Simple systems are disjoint from Gaussian systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove the theorem promised in the title. Gaussians can be distinguished from simple maps by their property of divisibility. Roughly speaking, a system is divisible if it has a rich supply of direct product splittings. Gaussians are divisible and weakly mixing simple maps have no splittings at all so they cannot be isomorphic. The proof that they are disjoint consists of an elaboration of this idea, which involves, among other things, the notion of virtual divisibility, which is, more or less, divisibility up to distal extensions. The theory of Kronecker Gaussians also plays a crucial role.
Słowa kluczowe
Czasopismo
Rocznik
Tom
133
Numer
3
Strony
249-256
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-09-08
poprawiono
1998-09-04
Twórcy
  • Department of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland, mlem@mat.uni.torun.pl
Bibliografia
  • [C,F,S] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer, Berlin, 1982.
  • [G,H,R] E. Glasner, B. Host and D. Rudolph, Simple systems and their higher order self-joinings, Israel J. Math. 78 (1992), 131-142.
  • [I,L,R,S] A. Iwanik, M. Lemańczyk, T. de la Rue et J. de Sam Lazaro, Quelques remarques sur les facteurs des systèmes dynamiques gaussiens, Studia Math. 125 (1997), 247-254.
  • [J,L,M] A. del Junco, M. Lemańczyk and M. K. Mentzen, Semisimplicity, joinings and group extensions, ibid. 112 (1995), 141-164.
  • [J,R] A. del Junco and D. Rudolph, On ergodic actions whose self-joinings are graphs, Ergodic Theory Dynam. Systems 7 (1987), 531-557.
  • [L,P,Th] M. Lemańczyk, F. Parreau and J.-P. Thouvenot, Gaussian automorphisms whose ergodic self-joinings are Gaussian, preprint.
  • [Th1] J.-P. Thouvenot, Some properties and applications of joinings in ergodic theory, in: Ergodic Theory and its Connections with Harmonic Analysis (Proc. Alexandria Conference), K. E. Petersen and I. Salama (eds.), London Math. Soc. Lecture Note Ser. 205, Cambridge Univ. Press, Cambridge, 1995, 207-235.
  • [Th2] J.-P. Thouvenot, Utilisation des processus gaussiens en théorie ergodique, preprint.
  • [Th3] J.-P. Thouvenot, The metrical structure of some Gaussian processes, in: Proc. Conf. on Ergodic Theory and Related Topics II (Georgenthal, 1986), Teubner Texte Math. 94, Teubner, Leipzig, 1987, 195-198.
  • [V] W. A. Veech, A criterion for a process to be prime, Monatsh. Math. 94 (1982), 335-341.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv133i3p249bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.