The Topology of Transport Through Planar Lyapunov Orbits

Abstract

An investigation of the topology of flow in the equilibrium region of the Planar Circular Restricted Three-Body Problem is presented. By utilizing a homeomorphic mapping we are able to visualize trajectories in the energy surface directly, giving insight into the governing role of invariant manifolds. We show that manifolds govern the flow of objects by physically blocking trajectories exterior to the manifold tubes in the energy surface from transiting. We demonstrate that transit orbits must flow inside invariant manifolds and pass through Lyapunov orbits in phase space, although they may appear to wander outside when projected in configuration space. Through a numerical investigation of transit orbits, we show manifolds govern the flow of objects over a wider range of energies than previously proven, controlling transit for energies at least as high as C = C(L_5).

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