Abstract
The behavior of fixed points on the surface of sections of two differential equations were studied. The first one, a particle in a standing wave field, exhibits universal bifurcation sequences, followed by the restabilization of some fixed points. The second, the undamped driven Duffing oscillator, produces more complex behavior with remerging bifurcations and other nonuniversal features. Some of these features can be ascribed to interactions between separate periodic orbits and bifurcation trees.
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