I have to demonstrate the following statement: "Consider a planar Hamiltonian System, with function of Hamilton H. Let be C the connected component of a level curve $\{H=c\}$ Suppose that: C is not empty, compact and don't contains any equilibrium point. Then C is the image of a periodic orbit".
I have prove that C contains the image of a periodic orbit, but i'm not able to demonstrate that the equal holds...
