Geodesic
Asymptotic Solution of the Autoresonance Problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 429-438 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the problem of forced oscillations near a stable equilibrium of a two-dimensional nonlinear Hamiltonian system of equations. A given exciting force is represented as rapid oscillations with a small amplitude and a slowly varying frequency. We study the conditions under which such a perturbation makes the phase trajectory of the system recede from the original equilibrium point to a distance of the order of unity. To study the problem, we construct asymptotic solutions using a small amplitude parameter. We present the solution for not-too-small values of time outside the original boundary layer.
Keywords: nonlinear oscillations, resonance, asymptotic approximation, averaging. 
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L. A. Kalyakin. Asymptotic Solution of the Autoresonance Problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 429-438. http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a8/

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