  We treat the problem of characterizing in a systematic way the qualitative
features of two-dimensional dynamical systems. To that end, we construct a
representation of the topological features of phase portraits by means of
diagrams that discard their quantitative information. All codimension 1
bifurcations are naturally embodied in the possible ways of transitioning
smoothly between diagrams. We introduce a representation of bifurcation curves
in parameter space that guides the proposition of bifurcation diagrams
compatible with partial information about the system.
