  In this article it is proved that an analytical planar vector field with a
non-degenerate center at $(0,0)$ is analytically conjugate, in a neighborhood
of $(0,0)$, to a Hamiltonian vector field of the form
$y\frac{\partial}{\partial x}-V'(x)\frac{\partial}{\partial y}$, where $V$ is
an analytic function defined in a neighborhood of the origin such that
$V(0)=V'(0)=0$ and $V''(0)>0.$
