Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural hamiltonian systems (Q1073248)

The author considers a mechanical system, that is, a Hamiltonian system with \(H(p,q)=(1/2)| p|^ 2+V(q)\), \(p,q\in {\mathbb{R}}^ n\), \(V\in {\mathbb{C}}^ 2({\mathbb{R}}^ n)\), and proves that if the set \(\Omega =\{q\in {\mathbb{R}}^ n|\) \(V(q)<h\}\) is bounded and non empty then the mechanical system has at least one periodic solution of energy \(H=h\).