MathPhys seminar Wednesday, November 3, 3:30p, 228 Kerchof:
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Tadashi Tokieda
(University of Illinois at Urbana-Champaign
and Universite du Quebec a Montreal)
"Perturbation Theory for symmetric Hamiltonian systems"
Abstract:
The problem of persistence, bifurcation, stability of periodic
orbits and equilibria is of special importance in perturbation
theory, and many results are known (e.g., Poincare', Weinberg,
Moser). We generalize thse results to systems having symmetries
given by a Hamiltonian action of a Lie group. Here the natural
objects of study are _relative periodic orbits_ (orbits that are
closed up to group action) and _relative equilibria_. We derive
a recipe for reducing the theory to the classical theory, which
works even in the hard case when we reduce at a singular value of
the moment map (as we often must in real life). Plane vortices
are discussed as examples; moreover, some of their exact
solutions show that the hypothesis in our recipe is tight.
[joint work with Lerman and Montaldi]
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Tadashi will be here Monday morning to Wednesday afternoon. His
main interest is symplectic geometry.