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Work in progress, plans

We have found a generalization of the method for problems involving
several oscillators.

We are planning to apply it to the problem
with
. In
two limits (
where the two Fourier modes decouple and
where )
we have an additional constant of motion.

By increasing the energy, we can observe bifurcations
in the stability of periodic solutions illustrated below.

We plan to study this classical instability in terms of small denominators
appearing in the perturbative series. We plan to study its quantum
counterpart (degeneracies) perturbatively and confront this study
with numerical results.
Figure 7: Poincaré sections for E=0.3055
Figure 8: Poincaré sections for E=0.34
Yannick Meurice
Tue Dec 10 22:51:23 CST 2002