By plotting surface of section, we get many island like surfaces.
I suggest you follow https://arc.aiaa.org/doi/abs/10.2514/1.46400?journalCode=jgcd
http://www.mat.unimi.it/users/sansotte/labmodmat/halo/193.pdf
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.972.1557&rep=rep1&type=pdf
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