Second order shadowing approximations for passage through resonance and capture at resonance
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The phenomenon of "passage through resonance" and "capture at resonance" is studied from the shadowing point of view. Second order approximations are given by a patching method for the case when the resonance zone contains saddle points and sinks. In shadowing, one gives up the attempt to find approximate solution to specified initial value problems, and instead looks simply for approximate solutions to the differential equation which are uniformly close to "some" exact solution for the entire time spent in the resonance zone.