Orbital stability of spherical galactic models
  We consider the three dimensional gravitational Vlasov Poisson system which
is a canonical model in astrophysics to describe the dynamics of galactic
clusters. A well known conjecture is the stability of spherical models which
are nonincreasing radially symmetric steady states solutions. This conjecture
was proved at the linear level by several authors in the continuation of the
breakthrough work by Antonov in 1961. In a previous work (arXiv:0904.2443), we
derived the stability of anisotropic models under {\it spherically symmetric
perturbations} using fundamental monotonicity properties of the Hamiltonian
under suitable generalized symmetric rearrangements first observed in the
physics litterature. In this work, we show how this approach combined with a
{\it new generalized} Antonov type coercivity property implies the orbital
stability of spherical models under general perturbations.
