Conservative dynamics: unstable sets for saddle-center loops

We consider two-degree-of-freedom Hamiltonian systems with a saddle-center loop, namely an orbit homoclinic to a saddle-center equilibrium (related to pairs of pure real, +/-v, and pure imaginary, +/-omegai, eigenvalues). We study the topology of the sets of orbits that have the saddle-center loop as their alpha and omega limit set. A saddle-center loop, as a periodic orbit, is a closed loop in phase space and the above sets are analogous to the unstable and stable manifolds, respectively, of a hyperbolic periodic orbit. (C) 2003 Elsevier Inc. All rights reserved.