RELATIVE EQUILIBRIA AND BIFURCATIONS IN A 2-D HAMILTONIAN SYSTEM IN RESONANCE 1:p.

In this work, we focus on a Hamiltonian system with two degrees of freedom whose normal form in a neighborhood of the equilibrium solution up to order two, corre- sponds to a subtraction of two harmonic oscillators in resonance 1:p, with p an odd number. We introduce appropriate coordinates in the reduced phase space in order to study the ex- istence of relative equilibria and bifurcations in terms of the free parameters of the system. We do this for to the simplest case, the resonance 1:3, and then we comment how these results can be extended for a resonance 1:p with p an odd number.