  The inviscid and thin accretion disc is a simple and well understood model
system in accretion studies. In this work, modelling such a disc like a
dynamical system, we analyse the nature of the fixed points of the stationary
solutions of the flow. We show that of the two fixed points, one is a saddle
and the other is a centre type point. We then demonstrate, using a simple but
analogous mathematical model, that a temporal evolution of the flow is a very
likely non-perturbative mechanism for the selection of an inflow solution that
passes through the saddle type critical point.
