H W Broer et al 1998 Nonlinearity 11 1569 doi:10.1088/0951-7715/11/6/009
Resonances in a spring-pendulum: algorithms for equivariant singularity theory
H W Broer, I Hoveijn, G A Lunter and G Vegter
Show affiliationsRecommended by J Laska
A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.
- PACS
- MSC
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37D50 Hyperbolic systems with singularities (billiards, etc.)
70H08 Nearly integrable Hamiltonian systems, KAM theory
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws
- Subjects
- Dates
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Issue 6 (November 1998)
Received 11 November 1997, in final form 22 July 1998
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Resonances in a spring-pendulum: algorithms for equivariant singularity theory
H W Broer et al 1998 Nonlinearity 11 1569
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