Periodic orbits in a Hamiltonian system of stellar type

We investigate the existence of periodic orbits in a perturbed Hamiltonian system of stellar type in 1:1 resonance. The perturbation consists of a potential of degree four with two real parameters. We determine six families of periodic orbits using reduction and averaging theories. Also, we characterize the stability of these orbits and their bifurcation curves in terms of the parameters. Finally, we show a complete picture of the choreographies of critical points originating the periodic orbits. •The study of stellar galaxies is based on exploring their orbits.•Some stellar models include perturbations of oscillators in 1:1 resonance.•The existence of periodic orbits in a perturbed Hamiltonian system in 1:1 resonance is investigated.