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2013
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# Larry Bates

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

## Publications:

 Cushman R., Bates L. Applications of the odd symplectic group in Hamiltonian systems 2011, vol. 16, no. 1-2, pp.  2-16 Abstract 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, no. 1-2, pp. 2-16 DOI:10.1134/S1560354710520011
 Bates L., Fasso F. An Affine Model for the Actions in an Integrable System with Monodromy 2007, vol. 12, no. 6, pp.  675-679 Abstract 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 DOI:10.1134/S1560354707060093