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.