MINI-CURSO DE GEOMETRÍA: JAMES MONTALDI (UNIVERSITY OF MANCHESTER, UK)

Título: Symmetric Hamiltonian Systems.

Fecha y hora: Lunes 22 y martes 23 de agosto, 11:00 horas.

Lugar: Aula de seminarios del IMATE en Oaxaca.

Temario:

1. Introduction: Hamilton's equations, symplectic manifolds.

2. Basic examples: N-body problem, Point vortices, Rigid body, Lagrange top, ...

3. Equilibria: stability and bifurcations.

4. Periodic orbits and Lyapunov centre theorem.

5. Symmetry (a): group actions preserving Hamilton's equations. Effect of symmetry on bifurcations and periodic orbits near equilibria.

6. Symmetry (b): Lie group actions, relative equilibria (or 'stationary motions'), conserved quantities and momentum map. Stability of relative equilibria. Bifurcations and (relative) periodic orbits.