RESONANCES IN A SPRING-PENDULUM - ALGORITHMS FOR EQUIVARIANT SINGULARITY THEORY

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symm etry (reversibility) is maintained. The reduction is handled by equiva riant singularity theory with a distinguished parameter, yielding an i ntegrable approximation of the Poincare map. This makes a concise desc ription of certain bifurcations possible. The computation of reparamet rizations from normal form to the actual system is performed by Grobne r basis techniques.