  For inviscid, rotational accretion flows, both isothermal and polytropic, a
simple dynamical systems analysis of the critical points has given a very
accurate mathematical scheme to understand the nature of these points, for {\em
any} pseudo-potential by which the flow may be driven on to a Schwarzschild
black hole. This allows for a complete classification of the critical points
for a wide range of flow parameters, and shows that the only possible critical
points for this kind of flow are saddle points and centre-type points. A
restrictive upper bound on the angular momentum of critical solutions has been
established. A time-dependent perturbative study reveals that the form of the
perturbation equation, for both isothermal and polytropic flows, is invariant
under the choice of any particular pseudo-potential. Under generically true
outer boundary conditions, the inviscid flow has been shown to be stable under
an adiabatic and radially propagating perturbtion. The perturbation equation
has also served the dual purpose of enabling an understanding of the acoustic
geometry for inviscid and rotational flows.
