STUDIES OF MELNIKOV METHOD AND TRANSVERSAL HOMOCLINIC ORBITS IN THE CIRCULAR PLANAR RESTRICTED THREE－BODY PROBLEM

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Studies of Melnikov method and transversal homoclinic orbits in the circular planar restricted three-body problem

Non-Hamiltonian systems containing degenerate fixed points obtained from twodegrees of freedom near-integrable Hamiltonian systems through non-canonicaltransformations are dealt with in this paper. Two criteria .for determining theexistence of transversal homoclinic and heteroclinic orbits are presented. By exploitingthese criteria the existence of the transversal homoclinic orbits and so, of thetransversal homoclinic tangle .phenomenon in the near-integrable circular planarrestricted three-body problem with sufficiently small mass ratio of the two primaries isproven. Under some assumptions, the existence of the transversal heleroclinic orbits isproven. The global qualitative phase diagram is also illustrated.