03-338 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) Jul 18, 03

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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.

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