Instability of equilibrium solutions of Hamiltonian systems with n-degrees of freedom under the existence of a single resonance and an invariant ray

Abstract

In this paper we prove the instability of one equilibrium point in an autonomous Hamiltonian system with n-degrees of freedom under two assumptions: the first is the existence of a single resonance of order s (without resonance of lower order, but it could exist resonance of greater order); and the second is the existence of an invariant ray solution of the truncated Hamiltonian system up to order s. Application of our main result to the satellite problem is considered.