ABSTRACT
Some tools, such as hammers and saws, are favorites because of their simplicity, importance and usefulness. The Poincare section is an example. A Poincare section (named after French mathematician Henri Poincare)' is merely a geometric picture of a trajectory's activity at a cross section of the attractor. The cross section is a slice or section through the attractor, transverse to the "flow" or bundle of trajectories (Fig. 18.1 ). "Transverse" here means "not parallel." The idea is to orient the imaginary cross section such that trajectories pierce it approximately normal to the surface of the section. (In fact, a Poincare section sometimes is called a surface of section.) The main purposes of a Poincare section are to provide a different view of the system's dynamics and possibly to help identify the type of attractor.
