Corollary 40.1.16.label Let $G$ be an infinite group and $G \curvearrowright X$ be a $G$-flow, then $X$ admits a recurrent point.
Proof. By Theorem 40.1.15, there exists $Y \subset X$ closed such that $G \curvearrowright X$ is minimal. In which case, Lemma 40.1.14 implies that every point in $Y$ is recurrent.$\square$
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