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 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