The Geometrical Point of View of Dynamical Systems: Background Material, Poincaré Maps, and Examples
Our main goal in the study of dynamical systems is simple. Given a specific dynamical system, give a complete characterization of the geometry of the orbit structure. If the dynamical system depends on parameters, then characterize the change in the orbit structure as the parameters are varied.
KeywordsVector Field Periodic Orbit Invariant Manifold Unstable Manifold Homoclinic Orbit
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