Heinz Hanßmann, Jan-Cees van der Meer
Algebraic methods for determining Hamiltonian Hopf bifurcations
in three-degree-of-freedom systems
(152K, PostScript, gzipped and uuencoded)

ABSTRACT.  When considering bifurcations, the type of bifurcation
is usually classified by comparing to standard situations or
normal forms. It is shown how Hamiltonian Hopf bifurcations can be
determined in three-degree-of-freedom systems, as is done in this
paper for the $3D$~H\'enon-Heiles family. After a careful
formulation of the local once reduced system in terms of properly
chosen invariants the system can be compared to the standard form
to determine the presence of non-degenerate Hamiltonian Hopf
bifurcations.