LAUSR

Abstract In this paper we study analytically the existence of two families of periodic orbits using the averaging theory of second order, and the finite and infinite equilibria of a generalized Henon-Heiles Hamiltonian system which includes the classical Henon-Heiles Hamiltonian. Moreover we show that this generalized Henon-Heiles Hamiltonian system is not C 1 integrable in the sense of Liouville–Arnol'd, i.e. it has not a second C 1 first integral independent with the Hamiltonian. The techniques that we use for obtaining analytically the periodic orbits and the non C 1 Liouville-Arnol'd integrability, can be applied to Hamiltonian systems with an arbitrary number of degrees of freedom.