I was reading a paper of Arnol'd ("Topological Properties of Eigenoscillations in Mathematical Physics") where he gives the following claim (hopefully I am stating it correctly).

One way to produce smooth 4-dimensional manifolds is to take some smooth, non-vanishing vector field $v$ on $\mathbb{R}^5$. The flow of this vector field defines a smooth $\mathbb{R}$-action on $\mathbb{R}^5$, and then we can just take the quotient of $\mathbb{R}^5$ by this action to produce some smooth 4-manifold $M$.

Arnol'd makes the interesting claim that, *given any exotic $\mathbb{R}^4$ we know about, it can be produced by a careful choice of this vector field)*.

Could anyone shed some light on the details of this construction?