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Periodic orbits in a Hamiltonian system of stellar type
Elsevier
2024
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.
1 resonance
Quartic potentials
Normalization and reduction
Averaging
Reduced space and invariants
Reeb’s theorem
Periodic orbits and linear stability
Bifurcations