This article is cited in 1 paper

Applications of the odd symplectic group in Hamiltonian systems

Richard Cushman, Larry Bates

Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada

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.

MSC: 70H12, 70K45

Received: 29.12.2009
Accepted: 23.02.2010

Language: English

DOI: 10.1134/S1560354710520011

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