Scattering of trajectories at a separatrix under autoresonance.

The subject of this paper is solutions of an autoresonance equation.We look for a connection between the parameters of the solution bounded as t ?-8, and the parameters of two two-parameter families of solutions as t ?8. One family consists of the solutions which are not captured into resonance, and another of those increasing solutions which are captured into resonance. In thiswaywe describe the transition through the separatrix for equations with slowly varying parameters and get an estimate for parameters before the resonance of those solutions which may be captured into autoresonance. [ABSTRACT FROM AUTHOR]