This article is inspired by two milestones in the study of non‐minimal group actions on the circle: Duminy's theorem about the number of ends of semi‐exceptional leaves, and Ghys' freeness result in real‐analytic regularity. Our first result concerns groups of real‐analytic diffeomorphisms with infinitely many ends: if the action is non‐expanding, then the group is virtually free. The second result is a Duminy type theorem for minimal codimension‐one foliations: either non‐expandable leaves have infinitely many ends, or the holonomy pseudogroup preserves a projective structure.

中文翻译：

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具有无限多个末端的组在圆周上进行分析性作用

本文的灵感来自于对圆上非最小群体行为的研究中的两个里程碑：关于半异常叶子末端数的Duminy定理，以及Ghys的自由度导致了实数分析的规律性。我们的第一个结果涉及具有无限多个目的的实解析微分群：如果动作是非展开的，则该群实际上是自由的。第二个结果是最小共维一叶的Duminy型定理：要么不可扩张的叶子有无限多个末端，要么完整性伪群保留了射影结构。