Dynamical systems and geometric numerical integration
by
Robert McLachlan
Massey University

Many of the "kinds of dynamics" that people study - complex dynamics, Hamiltonian dynamics, bifurcations with symmetry and so on - can be classified by the subgroup of the group of diffeomorphisms of phase space to which they belong. The simplest subgroups were studied by Lie and classified by Cartan, but amazingly, not all of them have been studied systematically, even though they include such popular examples as the Lorenz attractor and the Duffing oscillator. Part of the program of "geometric" numerical integration is to systematically design methods that lie in the relevant diffeomorphism group and have good qualitative long-time behaviour. I will report on what progress has been made so far and on the prospects for the future.

Date received: October 23, 2000

Copyright © 2000 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 # caek-73.