Emmanuel Roy
Joining primeness and disjointness from infinitely divisible systems.
Пт, 10/30/2009 - 16:01 — SomNambulAuthors: Emmanuel Roy, Mariusz Lemanczyk, François Parreau
Subjects: Dynamical Systems
AbstractWe show that ergodic dynamical systems generated by infinitely divisible
stationary processes are disjoint in the sense of Furstenberg with distally
simple systems and systems whose maximal spectral type is singular with respect
to the convolution of any two continuous measures.Poisson-Pinsker factor and infinite measure preserving group actions.
Ср, 09/09/2009 - 22:08 — SomNambulAuthors: Emmanuel Roy
Subjects: Dynamical Systems
AbstractWe solve the question of the existence of a Poisson-Pinsker factor for
conservative ergodic infinite measure preserving action of a countable amenable
group by proving the following dichotomy: either it has totally positive
Poisson entropy (and is of zero type), or it possesses a Poisson-Pinsker
factor. If G is abelian and the entropy positive, the spectrum is absolutely
continuous (Lebesgue countable if G=\mathbb{Z}) on the whole L^{2}-space in the
first case and in the orthocomplement of the L^{2}-space of the Poisson-Pinsker
factor in the second.
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