Periodic orbit families near the 4 : 1 jovian resonance

An enlarged averaged Hamiltonian is introduced to compute several families of periodic orbits of the planar elliptic 3-body problem, in the Sun-Jupite r-Asteroid system, near the 4:1 resonance. Four resonant critical point fam ilies are found and their stability is studied. The families of symmetric p eriodic orbits of the elliptic problem appear near the corresponding fixed points computed in this model. There is a good agreement for moderate eccen tricity of the asteroid for three of these families, whereas the remaining family cannot be considered as a family of periodic orbits of the real mode l.