Minicurso - 4 aulas

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