Symplectic Methods in the Numerical Search of Orbits in Real-Life Planetary Systems

DOI10.1137/22m1500459arXiv2206.00627OpenAlexW4389339788MaRDI QIDQ6187521

Unnamed Author, Agustin Moreno, Urs Adrian Frauenfelder

Publication date: 15 January 2024

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.00627

zbMATH Keywords

periodic orbitsthree-body problemHamiltonian systemsbifurcationssymplectic methodsnumerics

Mathematics Subject Classification ID

Three-body problems (70F07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Computational methods for bifurcation problems in dynamical systems (37M20) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07)

Cites Work

• The Conley conjecture
• Morse theory for Lagrangian intersections
• Witten's complex and infinite dimensional Morse theory
• The Maslov index for paths
• The restricted three-body problem and holomorphic curves
• Symplectic fixed points and holomorphic spheres
• The Hörmander index of symmetric periodic orbits
• New aspects in the theory of stability of Hamiltonian systems
• Linear stability of symplectic maps
• The unregularized gradient flow of the symplectic action
• A relative morse index for the symplectic action
• Cuplength estimates on lagrangian intersections
• Stability of periodic orbits in the elliptic, restricted three-body problem.
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