Abstract
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, ± ν, and pure imaginary, ± ωi, eigenvalues). We study the topology of the sets of orbits that have the saddle-center loop as their α and ω 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.
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