TY  - JOUR
A1  - Kiselev, Oleg
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Scattering of trajectories at a separatrix under autoresonance
JF  - Journal of mathematical physics
N2  - 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 -> -infinity, and the parameters of two two-parameter families of solutions as t -> infinity. One family consists of the solutions which are not captured into resonance, and another of those increasing solutions which are captured into resonance. In this way we 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. (C) 2014 AIP Publishing LLC.
Y1  - 2014
U6  - https://doi.org/10.1063/1.4875105
SN  - 0022-2488
SN  - 1089-7658
VL  - 55
IS  - 6
PB  - American Institute of Physics
CY  - Melville
ER  -