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We consider Hamiltonian systems near equilibrium that can be (formally) reduced to one degree of freedom. Spatio-temporal symmetries play a key role. The planar reduction is studied by equivariant singularity theory with distinguished parameters. The method is illustrated on the conservative spring-pendulum system near resonance, where it leads to integrable approximations of the iso-energetic Poincaré map. The novelty of our approach is that we obtain information on the whole dynamics, regarding the (quasi-) periodic solutions, the global configuration of their invariant manifolds, and bifurcations of these. Copyright © 1998 Elsevier Science B.V. All rights reserved.

Original publication

DOI

10.1016/S0167-2789(97)00202-9

Type

Conference paper

Publication Date

01/01/1998

Volume

112

Pages

64 - 80