Poincaré First Return Map

Another tool which illustrates the interesting dynamics of Rössler's attractor is the Poincaré first return map. We again take a cross-section of the band by cutting through it with a plane perpendicular to the flow (for our purposes the portion of the $y$-$z$ plane with $y<0$ works well). We then record the $y$-value of a trajectory when it crosses our plane and graph it against the $y$-value of the next time the trajectory crosses the section. In this way we can investigate the the mixing which is done by the ``twist'' in the attractor.