= Melnikov energy-balance method
{c}
For a weak perturbation of a planar <Hamiltonian system>, integrate the first-order <orbital derivative> of the Hamiltonian along an unperturbed homoclinic orbit. This measures the first-order separation of stable and unstable manifolds on a transverse section. A simple zero as a parameter varies permits a nearby homoclinic connection by the implicit function theorem. The resulting leading balance is not a claim that the unperturbed separatrix remains an exact orbit after perturbation.
Back to article page
