Abstract
The existence and stability of periodic solutions for the two-dimensional system x′=f(x)+ɛg(x,α), 0<ɛ≪1, α∈R whose unperturbed system is Hamiltonian can be decided by using the signs of Melnikov's function. The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with double zero eigenvalues.
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