The three-body problem as a geodesic billiard map with singularities

DOI10.1016/J.CNSNS.2020.105238zbMath1461.37062OpenAlexW3008389346MaRDI QIDQ2204517

Yanyan Li

Publication date: 15 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2020.105238

zbMATH Keywords

three-body problemPoincaré mapgeodesic billiardsJacobi-Maupertuis metric

Mathematics Subject Classification ID

Three-body problems (70F07) Applications of differential geometry to physics (53Z05) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (1)

Loose ends in a strong force 3-body problem

Cites Work

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• No hyperbolic pants for the 4-body problem with strong potential
• Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki
• Poncelet Porisms and Beyond
• The Three-Body Problem and the Shape Sphere
• Periodic three-body orbits with vanishing angular momentum in the Jacobi–Poincaré ‘strong’ potential
• Billiards on constant curvature spaces and generating functions for systems with constraints
• Realizing all reduced syzygy sequences in the planar three-body problem
• The three-body problem and equivariant Riemannian geometry
• Fitting hyperbolic pants to a three-body problem
• Riemannian geometry

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