Around King's Rank-One theorems: Flows and Z^n-actions

Élise Janvresse (1) , Thierry de La Rue (1) , Valery Ryzhikov (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 Faculty of Mechanics and Mathematics

We study the generalizations of Jonathan King's rank-one theorems (Weak-Closure Theorem and rigidity of factors) to the case of rank-one R-actions (flows) and rank-one Z^n-actions. We prove that these results remain valid in the case of rank-one flows. In the case of rank-one Z^n actions, where counterexamples have already been given, we prove partial Weak-Closure Theorem and partial rigidity of factors.

Mots clés: Rank-one actions; Weak Closure Theorem; Factors; Joinings

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Élise Janvresse, Thierry de La Rue, Valery Ryzhikov. Around King's Rank-One theorems: Flows and Z^n-actions. Dynamical Systems and Group Actions, AMS, pp.143-161, 2012, Contemporary Mathematics, vol 567, 978-0-8218-6922-2. ⟨10.1090/conm/567⟩. ⟨hal-00614548v3⟩