Larry Bates

Calgary, Alberta, T2N 1N4 Canada
Department of Mathematics and Statistics, University of Calgary


Cushman R., Bates L.
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.
Keywords: Hamiltonian systems, periodic orbits, odd symplectic normal forms
Citation: Cushman R., Bates L.,  Applications of the odd symplectic group in Hamiltonian systems, Regular and Chaotic Dynamics, 2011, vol. 16, nos. 1-2, pp. 2-16
Bates L., Fasso F.
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.
Keywords: monodromy, completely integrable systems
Citation: Bates L., Fasso F.,  An Affine Model for the Actions in an Integrable System with Monodromy, Regular and Chaotic Dynamics, 2007, vol. 12, no. 6, pp. 675-679

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