Preprint No.
A-01-11
Claudia Wulff
Persistence of relative equilibria in
Hamiltonian systems with non-compact symmetry
Abstract:
We prove new results on the persistence of Hamiltonian relative equilibria with generic
velocity-momentum pairs in the case of non-compact non-free group actions and taking into
account time reversibility. Our starting point is a relative equilibrium which is non-degenerate modulo
isotropy which, in the case of a generic momentum implies persistence of the given relative
equilibrium to all nearby momentum values with the same isotropy. We show that the analysis of the
persistence problem involves the study of a singular algebraic variety which is determined solely by
the symmetry group of the problem. We present persistence results for relative equilibria with
velocity-momentum pairs which are regular points of this variety and give sufficient conditions for a
velocity-momentum pair to be regular. We apply our results to relative equilibria of Euclidean
equivariant systems, including models of rigid bodies in fluids.
Keywords:
Mathematics Subject Classification (MSC2000):
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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