Contact geometry of the restricted three‐body problem

2010/10/11 by Peter Albers, Urs Frauenfelder, Otto van Koert +2 · 47 citations
Engineering · Mathematics · Physics and Astronomy · #Contact geometry #Control and Stability of Dynamical Systems #Geometry and topology #Planar #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control #Topology (electrical circuits) #Type (biology) #math.DS #math.GT #math.SG

paper · pdf · doi:10.1002/cpa.21380

published in Communications on Pure and Applied Mathematics 65(2), 229-263 (Wiley) · 29 pages, 1 figure

arxiv created 2010/10/11 · openalex publication_date 2011/10/20 · arxiv updated 2012/08/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Abstract We show that the planar circular restricted three‐body problem is of restricted contact type for all energies below the first critical value (action of the first Lagrange point) and for energies slightly above it. This opens up the possibility of using the technology of contact topology to understand this particular dynamical system. © 2011 Wiley Periodicals, Inc.

Citations

• Regularization of kepler's problem and the averaging method on a manifold
• Pseudo holomorphic curves in symplectic manifolds

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