What is a Poincaré section?
As I see it, the goal of a Poincaré section is to detect some sort of structure in the attractor. For a Poincaré section, take an attractor and an arbitrary plane which cuts the attractor into two pieces. The orbits which comprise the attractor cross the plane many times. Plot the intersections of the orbits and the Poincaré plane, although only plot the intersections which occur in one direction (crossing from the “bottom” side to the “top” side for example). This is the Poincaré section, which can reveal structure of the attractor. Another sort of Poincaré section is when you consider a natural period of the attractor (say, from the fundamental frequency which you could find using a power spectrum).
