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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.



Kevin Kesseler 2003-07-24