Contact Geometry of the Restricted Three-Body Problem on \mathbbS²

2024/11/16 by Kürşat Yilmaz, Yilmaz, Kursat, Alessandro Arsie +1
Engineering · Mathematics · #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Spacecraft Dynamics and Control #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2411.10885

openalex publication_date 2024/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the contact geometry of the connected components of the energy hypersurface, in the symmetric restricted 3-body problem on \mathbbS², for a specific type of motion of the primaries. In particular, we show that these components are of contact type for all energies below the first critical value and slightly above it. We prove that these components, suitably compactified using a Moser-type regularization are contactomorphic to Rℙ³ with its unique tight contact structure or to the connected sum of two copies of it, depending on the value of the energy. We exploit Taubes' solution of the Weinstein conjecture in dimension three, to infer the existence of periodic orbits in all these cases.

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