Consecutive collision orbits in the restricted three-body problem above the first critical energy value

2025/06/02 by Kang, Jungsoo, Kevin Ruck, Ruck, Kevin · 1 citation
Engineering · Physics and Astronomy · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2506.01735

openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we study the planar circular restricted three-body problem for energy levels slightly above the first critical value. We first observe that the energy hypersurfaces in the Birkhoff regularization corresponding to these energy levels are of contact type. Then, using a version of Rabinowitz Floer homology, we establish the existence of either a periodic symmetric collision orbit or infinitely many symmetric consecutive collision orbits. Furthermore, by an analytic continuation argument, for generic mass ratios and energy levels, we prove that there is no periodic symmetric collision orbit with odd number of collisions. This in turn implies the existence of at least two symmetric consecutive collision orbits.

Citations

• Tate Homology and Powered Flybys
• J⁺-invariants for planar two-center Stark-Zeeman systems
• Existence of either a periodic collisional orbit or infinitely many consecutive collision orbits in the planar circular restricted three-body problem
• Quasi-periodic Almost-collision Orbits in the Spatial Three-Body Problem
• Topological methods in 3-dimensional contact geometry
• Lagrangian Rabinowitz Floer homology and twisted cotangent bundles
• The Maslov index for paths
• Regularization of kepler's problem and the averaging method on a manifold

Cited by

• Wrapped Floer homology and the circular restricted three-body problem

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