Quasi-disjointness in topological dynamics
Dynamical Systems
2026-05-29 v1
Abstract
Motivated by Berg's notion of quasi-disjointness for ergodic systems, we introduce and investigate the concept of quasi-disjointness for minimal systems. Several equivalent characterizations are provided. We prove that quasi-disjointness is preserved under taking factors, proximal extensions, and group extensions. As a consequence, we establish that every minimal {\bf PI} system is quasi-disjoint from all minimal systems. In addition, some variant of quasi-disjointness, namely strong quasi-disjointness is also introduced and examined. Particularly, we prove that each {\bf AI} system is strongly quasi-disjoint from all minimal systems.
Cite
@article{arxiv.2605.30066,
title = {Quasi-disjointness in topological dynamics},
author = {Hui Xu and Xiangdong Ye},
journal= {arXiv preprint arXiv:2605.30066},
year = {2026}
}