Finite $C^\infty$-actions are described by one vector field
  In this work one shows that given a connected $C^\infty$-manifold $M$ of dimension $\geq 2$ and a finite subgroup $G\subset \Diff(M)$, there exists a complete vector field $X$ on $M$ such that its automorphism group equals $G\times \mathbb{R}$ where the factor $\mathbb{R}$ comes from the flow of $X$. 
F. J. Turiel and A. Viruel
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