Abstract
In a parameter dependent Hamiltonian system, an equilibrium might lose its stability via a socalled Hamiltonian Krein-Hopf bifurcation ([1], [12]): Two pairs of purely imaginary eigenvalues of the linearized system collide (1-1 resonance) and split off the imaginary axis into the complex plane. In the following we will refer to this scenario as the splitting case, see Figure 1. It is well known that in one parameter problems without external symmetry this is the only eigenvalue behavior that generically occurs in 1-1 resonances ([4], [9], [10]).
Research is supported by the Deutsche Forschungsgemeinschaft and by NSF DMS-9101836.
Research partially supported by a Humboldt award and DOE Contract DE-FG03-88ER25064.
Supported in part by NSF DMS-9101836
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© 1992 Birkhäuser Verlag Basel
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Dellnitz, M., Marsden, J.E., Melbourne, I., Scheurle, J. (1992). Generic Bifurcations of Pendula. In: Allgower, E.L., Böhmer, K., Golubitsky, M. (eds) Bifurcation and Symmetry. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 104. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7536-3_10
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DOI: https://doi.org/10.1007/978-3-0348-7536-3_10
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