Generalized van der Waals Hamiltonian: Periodic orbits and $C^1$ nonintegrability

The aim of this paper is to study the periodic orbits of the generalized van der Waals Hamiltonian system. The tool for studying such periodic orbits is the averaging theory. Moreover, for this Hamiltonian system we provide information on its ${\mathcal{C}}^1$ nonintegrability, i.e., on the existence of a second first integral of class ${\mathcal{C}}^1$.