Around King's Rank-One theorems: Flows and Zⁿ-actions

2011/08/13 by Élise Janvresse, Thierry de la Rue, Janvresse, Élise +3 · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1108.2767

openalex publication_date 2011/08/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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 Zⁿ-actions. We prove that these results remain valid in the case of rank-one flows. In the case of rank-one Zⁿ actions, where counterexamples have already been given, we prove partial Weak-Closure Theorem and partial rigidity of factors.

Cited by

• On Local Rank, Joinings and Asymptotic Properties of Measure-Preserving Actions

Related

• On Local Rank, Joinings and Asymptotic Properties of Measure-Preserving Actions
• Hyperbolic actions of higher-rank lattices come from rank-one factors
• KAM rigidity for partially hyperbolic affine Z^k actions on the torus with a rank one factor
• On measure-preserving rank one transformations
• Boundary actions by higher-rank lattices: Classification and embedding in low dimensions, local rigidity, smooth factors