Finite $C^{\mathrm{\infty }}$-actions are described by one vector field

In this work one shows that given a connected $C^{\mathrm{\infty }}$-manifold $M$ of dimension $\ge 2$ and a finite subgroup $G\subset \text{Diff}(M)$, 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 $X$.