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Algebraic Methods for Determining Hamiltonian Hopf Bifurcations in Three-Degree-of-Freedom Systems |
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| Authors: | Heinz?Han?mann mailto:Heinz@iram.rwth-aachen.de" title=" Heinz@iram.rwth-aachen.de" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Jan-Cees?van?der?Meer |
| Affiliation: | (1) Institut f ür Reine und Angewandte Mathematik der RWTH Aachen, 52056 Aachen, Germany;(2) Faculteit Wiskunde en Informatica, Technische Universiteit Eindhoven, Eindhoven, The Netherlands |
| Abstract: | A method is sketched to determine the presence of non-degenerate Hamiltonian Hopf bifurcations in three-degree-of-freedom systems by putting the bifurcation into standard form. Detailed computations are performed for the non-trivial example of the 3D Hénon–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 by the application of singularity theoretic results. |
| Keywords: | Hamiltonian system bifurcation normal form reduction singularity Hé non-Heiles family Hamiltonian Hopf relative equilibria |
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