Calgary, Alberta, T2N 1N4 Canada
Department of Mathematics and Statistics, University of Calgary
Cushman R., Bates L.
Applications of the odd symplectic group in Hamiltonian systems
2011, vol. 16, no. 1-2, pp. 2-16
In this paper we give two applications of the odd symplectic group to the study of the linear Poincaré maps of a periodic orbits of a Hamiltonian vector field, which cannot be obtained using the standard symplectic theory. First we look at the geodesic flow. We show that the period of the geodesic is a noneigenvalue modulus of the conjugacy class in the odd symplectic group of the linear Poincaré map. Second, we study an example of a family of periodic orbits, which forms a folded Robinson cylinder. The stability of this family uses the fact that the unipotent odd symplectic Poincaré map at the fold has a noneigenvalue modulus.
Bates L., Fasso F.
An Affine Model for the Actions in an Integrable System with Monodromy
2007, vol. 12, no. 6, pp. 675-679
We give a standard model for the flat affine geometry defined by the local action variables of a completely integrable system. We are primarily interested in the affine structure in the neighborhood of a critical value with nontrivial monodromy.