Semester 1: General perturbaion theory
Canonical perturbaion theory: Hamilton-Jacobi method, acion-angle variables. The fundamental theorem of perturbaion theory, Delaunay's lunar theory and eliminaion method. Poincaré-Zeipel method. Theory of resonant perturbaions. Lie transform perturbaion theory. Superconvergent perturbaion theory. Ordered and chaoic moions: KAM theory.
Ordered and chaoic orbits in the restricted three-body problem. Lyapunov indicators. Poincaré mappings. Hénon-Heiles problem. Symplecic mappings, symplecic integrators.
Semester 2: Dynamics of planetary systems
Resonances of irst and second order. Resonant encounters, capture into and passing through a resonance. Muliple resonances.Resonances in the Solar System.
Dynamics of the Solar System: Moion of giant planets. Stability of the Solar System. Rotaion of the planets and moons. Dynamics of resonant asteroids.
Exoplanetary systems: Dynamical classiicaion of muliple planetary systems. Resonant, interacing and hierarchical systems. Planet-disk interacions. Stability of exoplanetary systems.
Semester 3: The three-body problem
The general three-body problem: Equaions of moion and irst integrals. The Lagrange-Jacobi equaion. Classiicaion of inal coniguraions. The Euler-Lagrange soluions.
The restricted three-body problem: Equaions of moion, the Jacobi-integral. Equilibrium soluions and their stability. Zero velocity curves. Regularizaion transformaions. Periodic and numerical soluions. The ellipic restricted three-body problem. The Hill-problem.
Semester 4: Theory of ariicial satellites
The gravitaional potenial. Terrestrial gravitaional perturbaions.
Lunisolar perturbaions. Non-gravitaional perturbaions.
