Restricted Three-Body Problem and Holomorphic Curves

Introduction.- Symplectic geometry and Hamiltonian mechanics.- Symmetries.- Regularization of two body collisions.- The restricted three body problem.- Contact geometry and the restricted three body problem.- Periodic orbits in Hamiltonian systems.- Periodic orbits in the restricted three body problem.- Global surfaces of section.- The Maslov Index.- Spectral flow.- Convexity.- Finite energy planes.- Siefring's intersection theory for fast finite energy planes.- The moduli space of fast finite energy planes.- Compactness.- Construction of global surfaces of section.- Numerics and dynamics via global surfaces of section.

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• Geometria diferencial e riemaniana
• Análise complexa, variáveis ??complexas

symplectic geometry;contact geometry;holomorphic curves;celestial mechanics;restricted three-body problem;global surfaces of section;symplectic dynamics