Dynamical Systems and Group Actions

2012/01/01 by Bowen, Lewis, Grigorchuk, Rostislav, Vorobets, Yaroslav · 1 citation
Mathematics · #Mathematical Dynamics and Fractals #Mathematics #Group action #Group (periodic table) #Pure mathematics #Dynamical systems theory #Algebra over a field

paper · doi:10.1090/conm/567

openalex publication_date 2012/01/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05

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.

Citations

• Rank one Z^d actions and directional entropy

Cited by

• Amenable group [wikipedia]