ABSTRACT
This chapter characterizes the possible structures of the attractors in bi-dimensional flows. It makes sense of the popularized statement ‘there is no chaos in bi-dimensional flows’. This characterization can be achieved in the form of a theorem (Poincaré–Bendixson theorem). The Pontryagin–Andronov theorem establishes conditions that are equivalent to structural stability for flows confined to a bi-dimensional disk. The chapter concludes the ‘elementary’ part of the analysis of dynamical systems. It gives special names to the sets of points in phase space bearing the asymptotic properties of the flow, studied the properties of these sets and considered some of the conditions in which the flow will tend to these sets.
