Simple systems are disjoint from Gaussian systems

• Autorzy: Andrés del Junco , Mariusz Lemańczyk
• 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.

Kategorie tematyczne

• 28D15: General groups of measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 133
• Numer: 3
• Strony: 249-256

Daty

wydano

1999

otrzymano

1997-09-08

poprawiono

1998-09-04

Twórcy

autor

Andrés del Junco

• Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1

autor

Mariusz Lemańczyk

• Department of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

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