Influence of planetary oblateness on Keplerian dynamics in magnetospheres and existence of invariant tori

The problem of the dynamics of a charged particle orbiting around a rotating magnetic planet is revisited, the goal being twofold. On the one hand the model takes into account, apart from the magnetic and the electric field, the gravitational potential of the planet where the effect of the planetary oblateness is also incorporated. The techniques used in this analysis include averaging with respect to the mean anomaly, reduction to the simplest possible reduced space, study of the possible relative equilibria with the occurring parametric bifurcations and the stability analysis of these equilibria using normal forms. Also, we prove the existence of KAM 3-tori of the original system from the relative equilibria that are elliptic points in the fully-reduced space.

► We include the perturbation caused by the planets oblateness, extending a previous work.
► A full analysis of the relative equilibria and their stability has been achieved.
► We determine the bifurcation lines in terms of the parameters. The bifurcation diagram has 16 regions.
► There exist invariant 2-tori reconstructed from the relative equilibria, with the same stability.
► There exist KAM 3-tori reconstructed from the elliptic relative equilibria.