# University of Toronto's Symplectic Geometry Seminar

May 10, 2007, 2:10pm

BA 6183

## Eva Miranda

### University Paul Sabatier

## Some geometrical aspects of integrable systems on symplectic
and Poisson manifolds

**Abstract: **
Given a regular compact orbit, L, of an integrable system on
a symplectic manifold, it is well-known due to Arnold-Liouville
theorem that the neighbouring orbits are given by a Hamiltonian torus
action by translations which, in its turn, yields action-angle
coordinates in a neighbourhood of L.
We will present some generalizations of this result first to the case
the orbit is singular of non-degenerate type in a symplectic manifold
and then to the case of integrable systems on Poisson manifolds. The
last part of the talk is based on joint work with Camille
Laurent-Gengoux and Pol Vanhaecke.