Identification of structures within higher dimension Poincaré maps relating to quasi-periodic transforming orbits (Q6573412)

This work is a numerical study of the spatial circular restricted three-body problem (CR3BP) via higher dimension Poincaré map. Two-dimensional Poincaré maps were widely used to conduct numerical exploration of the planar restricted three-body problem since Poincaré discovered the method in 1899, but in particular, since the nineteen sixties, when computers became readily available for such tasks to pioneers like Michel Henon.\N\NDue to the lack of integrals of motion other than the Jacobi Constant, the CR3BP is five dimensional. This in turn means that, in spite of the fact that a Surface of Sections reduces the problem by an additional dimension, one needs to visualize four-dimensional space. The authors utilize 3D heat maps (``4D Poincaré'') for this task. However, their approach suffers from the major problem that such maps are very difficult to interpret. In spite of these difficulties, it appears that the authors have been able to portray and examine 13 different quasi-periodic orbits as well as to identify some structures in the 4D Poincaré maps.