Poincaré Map
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High Quality Content by WIKIPEDIA articles! In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower dimensional subspace, called the Poincaré section, transversal to the flow of the system. More precisely, one considers a periodic orbit with initial conditions on the Poincaré section and observes the point at which this orbits first returns to the section, thus the name first recurrence map. The transversality of the…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower dimensional subspace, called the Poincaré section, transversal to the flow of the system. More precisely, one considers a periodic orbit with initial conditions on the Poincaré section and observes the point at which this orbits first returns to the section, thus the name first recurrence map. The transversality of the Poincaré section basically means that periodic orbits starting on the subspace flow through it and not parallel to it.