Transverse foliations in the rotating Kepler problem. (English) Zbl 1536.70011
The author constructs finite energy foliations (for all negative energies), and transverse foliations in the neighbourhoods of the circular orbits in the rotating Kepler problem, planar circular restricted thee-body problem (PC3BP). This paper has been a first step for its ultimate goal that is to recover and refine McGehee’s results on homoclinics and to establish a theoretical foundation to the numerical demonstration of the existence of a homoclinic-heteroclinic chain in the PCR3BP, using pseudoholomorphic curves. The author also presents an alternative way to obtain a transverse foliation whose pages are annuli.
Reviewer: Maria Gousidou-Koutita (Thessaloniki)
MSC:
| 70F07 | Three-body problems |
| 70K44 | Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics |
Keywords:
planar circular restricted thee-body problem; homoclinic-heteroclinic chain; planar circular orbitReferences:
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