Asymptotic behaviour of measure for captured trajectories into parametric autoresonance

Abstract

We study an asymptotic behaviour of parametric autoresonance for non-linear equation. Main result of this work is statement about asymptotic behaviour of measure for captured trajectories. To find this we obtain an asymptotic expansion for capture and asymptotic behaviour of splitted separatrices for intermediate small amplitudes. * Institue of mathematics Ufa science centre of RAS; ok@ufanet.ru 1 arXiv:1612.08426v1 [math.DS]

Autoresonance in oscillating systems with combined excitation and weak dissipation

“…Mathematical models associated with the autoresonance have been studied in many papers. See, for instance, [17][18][19][20][21], where the systems with external driving were analyzed, and [22][23][24][25][26], where the models of parametric autoresonance were investigated. The effect of a combined external and parametric excitation on the autoresonant capture in nonlinear systems was first studied in [27,28].…”