Structure theorems of commuting transformations and minimal $ \mathbb{R} $ -flows
Abstract
In this paper, we develop several structure theorems concerning commuting transformations and minimal $ \mathbb{R} $-flows. Specifically, we show that if $ (X, S) $, $ (X, T) $ are minimal systems with $ S $ and $ T $ being commutative, then they share an identical higher-order regionally proximal relation. Consequently, both $ (X, S) $ and $ (X, T) $ share the same increasing sequence of pro-nilfactors. For minimal $ \mathbb{R} $-flows, we introduce the concept of higher-order regionally proximal relations and nilfactors, and establish that nilfactors are characteristic factors for minimal $ \mathbb{R} $-flows, up to almost one to one extensions.
Fields of Study & Subjects
Advanced Algebra and Logic
semigroups and automata theory
Fuzzy and Soft Set Theory
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 52
- Issue
- 0
- Pages
- 70–114
- Publication date
- 1 January 2026