NONLINEAR STABILITY NEAR A 1: 3 RESONANCE

In this paper we investigate the evolution of the stability domain for a two degrees of freedom Hamiltonian system near a 1:3 resonance. In this way, it is proven that the lost of stability takes place when the size of the stability domain goes to zero. In fact, away of the 1:3 resonance, there always exists a stability domain which size diminishes as we approach the exact value of the resonance.