Resonant bifurcations from relative homoclinic cycles
by
Drs. R. Driesse
Korteweg-de Vries Institute for Mathematics (University of Amsterdam)
Coauthors: Ale Jan Homburg (Korteweg-de Vries Institute for Mathematics)

Heteroclinic cycles can be robust if forced by symmetry. The stability of these cycles depends on the

eigenvalues of the linearized equations around the fixed points. Neccessary and sufficient conditions can be shown

generically for heteroclinic cycles, but also nongenerically for homoclinic cycles. If we perterb the system so that the

eigenvalues do not satisfy the stability condition anymore, we speak of a resonant bifurcation. We show that an

asymptotically stable periodic orbit can exist after the bifurcation. These results hold for heteroclinic cycles in

three dimensions and homoclinic cycles in four dimensions.

Date received: July 5, 2007

Copyright © 2007 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 # cavl-04.