Poisson-Pinsker factor and infinite measure preserving group actions

Emmanuel Roy (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We 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.

Mots clés: Poisson suspensions; infinite ergodic theory; joinings

Domaines: Systèmes dynamiques [math.DS]

Emmanuel Roy. Poisson-Pinsker factor and infinite measure preserving group actions. Proceedings of the American Mathematical Society, 2010, 138 (06), pp.2087-2094. ⟨hal-00414147⟩