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Disjointness with all minimal systems under group actions

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arxiv 2212.07830 v3 pith:RS4PDAWS submitted 2022-12-15 math.DS

Hui Xu , Xiangdong Ye This is my paper · ORCID
classification math.DS
keywords minimaltransitivesystemsdisjointsystemdensegroupinfty
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abstract

Let $G$ be a countable discrete group. We give a necessary and sufficient condition for a transitive $G$-system to be disjoint with all minimal $G$-systems, which implies that if a transitive $G$-system is disjoint with all minimal $G$-systems, then it is $\infty$-transitive, i.e. $(X^k,G)$ is transitive for all $k\in\N$, and has dense minimal points. In addition, we show that any $\infty$-transitive $G$-system with dense distal points are disjoint with all minimal $G$-systems.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the denseness of distal points

    math.DS 2026-07 conditional novelty 7.0 of 10

    Distal points are dense in 2^G exactly when G admits an effective point-distal action; almost automorphic points are dense exactly when G is maximally almost periodic; only constant distal points exactly when G is min...

  2. On systems disjoint from all minimal systems

    math.DS 2025-04 conditional novelty 7.0 of 10

    A topological system is disjoint from every minimal system exactly when it has countably many dense minimal subsets each disjoint from it, with analogous residual-pair and distal characterizations.

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