Hamiltonian Systems Near Relative Periodic Orbits
Wulff, Claudia and Roberts, RM (2002) Hamiltonian Systems Near Relative Periodic Orbits Dynamical Systems, 1. pp. 1-43.
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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|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 :||23 Sep 2013 18:32|
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