A General Criterion for the Dynamical Stability of Anisotropic Newtonian Systems

The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations. Configurations that cannot exist in the isotropic regime can exist in the anisotropic one. Some applications of the criterion are also included.