  We survey the few exact results on the Stormer problem describing the
dynamics of charged particles in the Earth magnetosphere. The analysis of this
system leads to the the conclusion that charged particles are trapped in the
Earth magnetosphere or escape to infinity, and the trapping region is bounded
by a torus-like surface, the Van Allen inner radiation belt. In the trapping
region, the motion of the charged particles can be periodic, quasi-period or
chaotic. The three main effects observed in the Earth magnetosphere, radiation
belts, radiation aurorae and South Atlantic anomaly, are described in the
framework described here. We discuss some new mathematical problems suggested
by the analysis of the Stormer problem.
