Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor

The theory of bifurcation of limit cycles for perturbed Hamiltonian planar systems was discussed. A limit cycle bifurcates in the perturbed system from the periodic orbits of the unperturbed system. The analytical computation was performed for the bifurcated limit cycles from a Hamiltonian center perturbed by an arbitrary analytical vector field.