applications it may be instead convenient to construct a perturbative formalism based on two (or more) parameters, because the choice of background is crucial in having a manageable theory. The study of perturbations of stationary axisymmetric rotating stars (see [@kojimarev; @laf; @rsk] and references therein) is a good example. In this case, an analytic stationary axisymmetric solution is not known, at least for reasonably interesting equations of state. A common procedure is to treat axisymmetric stars using the so–called slow rotation approximation, so that the background is a star with spherical symmetry [@hartle; @hartlethorne]. In this approach the first order in $\Omega$ discloses frame dragging effects, with the star actually remaining spherical; $\Omega^2$ terms carry the effects of rotation on the fluid. This is intuitive from a Newtonian point of view, as rotational kinetic energy goes like $\Omega^{2}$. This approximation is valid for angular velocities $\Omega$ much smaller than the mass shedding limit $\Omega_K\equiv\sqrt{M/R_{star}^3}$, with typical values for neutron stars $\Omega_K\sim 10^3Hz$. Therefore the slow rotation approximation, despite the name, can still be valid for large angular velocities. In practice, the perturbative approach up to $\Omega^2$ is accurate for most astrophysical situations, with the exception of newly born neutron stars 