Mini-course: Symplectic Topology and Celestial Mechanics - Urs Frauenfelder - 01

Speaker: Urs Frauenfelder

Syllabus
- Hamiltonian Dynamics, Symplectic, Hamiltonian and Contact manifolds
- Symmetries and Noether's Theorem
- The Kepler Problem and its symmetries
- Time-dependent transformations
- The restricted three-body Problem in intertial and rotating coordinate systems
- Lagrange Points
- Hill's lunar Problem
- The direct and retrograde periodic orbits (existence of the retrograde via shooting according to Birkhoff)
- Periodic orbits of the rotating Kepler Problem
- Levi-Civita and Moser Regularization of the restricted three-body Problem
- Birkhoff's conjecture about existence of a disklike global surface of section bounded by the retrograde
- Brouwer's fixed point theorem and existence of direct orbits
- Annulus-like global surfaces of section and the Poincaré-Birkhoff theorem

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