The top figure illustrates a subset of the dynamics of the Circular Restricted Three Body Problem for a mass ratio of 0.3. The surface of section used to generate this map is y=0, and the initial conditions are chosen to be retrograde with respect to the motion of the primaries. In addition, the Jacobi Constant is set to approximately 3.90, slightly below that of L1. Frequency analysis can be used to understand the periodic and quasi periodic structures in this island. Points with a perpendicular crossing of the map are propagated and decomposed into their two fundamental frequencies. In the bottom figure, the ratio of these frequencies is plotted.
Click on one of the outlined stable islands to see how the frequency ratio reflects properties of the dynamics.

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