Dynamical Systems Seminar

Many problems in dynamics are described by well ordered motions subjet to periodic (or quasi-periodic perturbations). An important example will be the motion of a planet around the sun (according to Kepler laws) subject to the perturbations of the other planets.

One problem of fundamental practical importance is whether the small perturbations will accumulate over time or just average out.

The answer turns out to be rather complicated and depends on delicate number theoretic properties and regularity issues. Nevertheless, it is possible to get a geometric understanding of where the instability occurs. In some cases, one can take advantage of this accumulation of perturbations to make complicated maneouvers of spacecraft using the tides of the planets, which are free instead of expensive fuel.