That is, for any symplectomorphism $\psi: D^2 \to D^2$, there should be a time-dependent Hamiltonian H_t on D² such that the corresponding flow at time 1 is equal to $\psi$.

I found this in claim a paper, and I think it should be easy, but nothing comes to mind. I'd be happy with a reference to a page in McDuff-Salomon, but I couldn't find this there immediately.

Thanks!