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Hamiltonian Systems Near Relative Periodic Orbits

Wulff, Claudia and Roberts, RM (2002) Hamiltonian Systems Near Relative Periodic Orbits Dynamical Systems, 1. pp. 1-43.


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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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 8 April 2002
Uncontrolled Keywords : relative periodic orbits, equivariant Hamiltonian systems, noncompact groups
Additional Information : Published in the SIAM Journal on Applied Dynamical Systems, 1, 1-43. © 2002 Society for Industrial and Applied Mathematics.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:40
Last Modified : 16 Jan 2019 16:21

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