The main purpose of
this paper is to classify the dynamical systems on the plane which satisfy a
certain type of stability criterion. Such flows are referred to as dynamical
systems of characteristic 0+. The classification is based on the consideration
of three mutually exclusive and exhaustive cases: Dynamicaf systems of
characteristic 0+ which have no critical points. Those whose critical points form
nonempty compact sets, and those whose critical points do not form compact
sets.