A normally elliptic Hamiltonian bifurcation |
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| Authors: | H W Broer S N Chow Y Kim G Vegter |
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| Institution: | (1) Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands;(2) School of Mathematics, Georgia Institute of Technology, 30332 Atlanta, GA, USA;(3) Department of Mathematics, University of Ulsan, P.O. Box 18, 680-749 Ulsan, South Korea;(4) Department of Computing Science, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands |
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| Abstract: | A universal local bifurcation analysis is presented of an autonomous Hamiltonian system around a certain equilibrium point. This central equilibrium has a double zero eigenvalue, the other eigenvalues being in general position. Main emphasis is given to the 2 degrees of freedom case where these other eigenvalues are purely imaginary. By normal form techniques and Singularity Theory unfoldings are obtained, having  integrable approximations related to the Elliptic and Hyperbolic Umbilic CatastrophesDedicated to Klaus Kirchgässner on his sixtieth birthday |
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