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The Topology of Transport Through Planar Lyapunov Orbits*

机译：通过平面Lyapunov轨道传输的拓扑*

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An investigation of the topology of How 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 How 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).
机译：提出了如何在平面圆受限三体问题的平衡区域内进行拓扑的研究。通过使用同胚映射，我们能够直接可视化能量表面的轨迹，从而深入了解不变流形的控制作用。我们表明，歧管通过物理阻塞能量表面中歧管外部的轨迹来阻止传输，从而控制了对象的行为方式。我们证明了过渡轨道必须在不变流形内部流动并在相空间中通过Lyapunov轨道，尽管在构型空间中投影时它们可能看起来在外部徘徊。通过对过渡轨道的数值研究，我们显示了流形控制物体在比先前证明更广泛的能量范围内的流动，从而控制了至少高达C = C（L_5）的能量的过渡。

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