Slow manifolds in a singularly perturbed Hamiltonian system
by
Vassili Gelfreich
Mathematics Institute, University of Warwick
Coauthors: Lev Lerman (Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod)

Assume that a Hamiltonian system looses a part of its degrees of freedom in the following way: the motion in the slow component stops in the limit \epsilon --> 0. In this case, the small parameter enters the dynamics through the corresponding symplectic form instead of the Hamiltonian function. The slow manifold can be defined in the usual way, but unlike the general case the slow manifold can be normally elliptic for a generic Hamiltonian. We study a mechanism, which destroys the normally elliptic slow manifold and use a specially developed averaging techniques to study the dynamics nearby.

Date received: May 9, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calh-22.