Symplectic Topology and Celestial Mechanics
IMPA, August 12 - 14 2019
Program
| Aug 12 (Mon) | Aug 13 (Tue) | Aug 14 (Wed) | |
| 9:30am - 10:00am |
Urs Frauenfelder (auditório 3) |
||
| 10:00am-11:00am |
Urs Frauenfelder (auditório 3) |
Urs Frauenfelder (auditório 3)
|
Pedro Salomão (auditório 3) |
| 11:00am - 11:30am |
Urs Frauenfelder (auditório 3) |
Umberto Hryniewicz (auditório 3) |
Pedro Salomão (auditório 3) |
| 11:00am-12:30pm |
Umberto Hryniewicz (auditório 3) |
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
- 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
- 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
- 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