University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Abstract
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.
