Preprint No. A-00-26

Claudia Wulff, Mark Roberts

Hamiltonian systems near relative periodic orbits

Abstract: We give explicit differential equations for a symmetric Hamiltonian vector field near a relative periodic orbit. These decompose the dynamics into periodically forced motion in a Poincaré section transversal to the relative periodic orbit, which in turn forces motion along the group orbit. The structure of the differential equations inherited from the symplectic structure and symmetry properties of the Hamiltonian system is described and the effects of time reversing symmetries are included. Our analysis yields new results on the stability and persistence of Hamiltonian relative periodic orbits and provides the foundations for a bifurcation theory. The results are applied to a finite dimensional model for the dynamics of a deformable body in an ideal irrotational fluid.

Keywords:

Mathematics Subject Classification (MSC91):

Language: ENG

Available:

Contact: Claudia Wulff, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (wulff@math.fu-berlin.de)

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