Method II: The energy-momentum map

H. Broer, I. Hoveijn, G. Lunter, G. Vegter


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In this chapter we apply the energy–momentum map reduction method to the same class of systems as in Chap. 2, namely two degree-of-freedom systems with optional symmetry, near equilibrium and close to resonance. We calculate the tangent space and nondegeneracy conditions for the 1:2, 1:3 and 1:4 resonances starting from a Birkhoff normalized Hamiltonian. The case of the spring-pendulum close to 1:2 resonance is treated in more detail. We arrive at a polynomial model which is different from the one found in Chap. 2, and which has an additional saddle–node bifurcation.
Originele taal-2English
UitgeverijUniversity of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Aantal pagina's24
StatusPublished - 2003

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