Resonance in Hamiltonian Systems
Sven Schmidt
Loughborough University
I am going to talk about a two degree-of-freedom (2-DOF) Hamiltonian system whose linear frequencies are in 1:2 resonance. After applying singular reduction to the normal form expansion, I will show that the problem can reduced to 1-DOF. This geometric approach allows us to study the system in a reduced phase space. Of particular interest is the behavior of the reduced period, T, and the rotation number, W, near the singular point; these are strongly influenced by the resonance. If time permits, I'll briefly mention monodromy, generalization to q:p resonances, and vanishing twist