Stability of Spherically Symmetric Steady States in Galactic Dynamics¶against General Perturbations

Certain steady states of the Vlasov-Poisson system can be characterized as minimizers of an energy-Casimir functional, and this fact implies a non-linear stability property of such steady states. In previous investigations by Y. Guo and G. Rein, stability was obtained only with respect to spherically symmetric perturbations. In the present investigation we show how to remove this non-physical restriction.