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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