Unsupervised approach to detect interconnections between unstable resonant orbits

The study of resonant flybys has been increasingly addressed by incorporating three-body effects in early stages of complex tour designs. In the past, a resonant transition mechanism revealed the existence of a close interplay between the invariant manifolds associated with unstable resonant orbits at certain energies, coined as interconnection, and has been used to benefit from large-scale natural transport across phase space. However, the state-of-the-art has focussed either on point resonances at few energies, or on promoting resonant transitions via heteroclinic connections that generally do not occur in the most direct way. This paper intends to continue the work of previous researchers and fill a gap left behind, by carrying out a systematic analysis to search for interconnections between fifteen resonant families at multiple energy levels, covering the spectrum of resonances between the secondary in the CR3BP Jupiter–Europa system and Ganymede. To this end, an unsupervised procedure is implemented using standard dynamical systems techniques, and including a simple geometric detection method to capture the clearest homoclinic connections, so that the explicit use of Poincar´e maps is not necessary. The results presented here can potentially be used to train deep neural networks in order to mitigate the computational burden.