Asymptotic behaviour of measure for captured trajectories into parametric autoresonance

TL;DR

This paper investigates the long-term behavior of the measure of trajectories captured in parametric autoresonance for nonlinear systems, providing asymptotic expansions and analysis of separatrix splitting at small amplitudes.

Contribution

It introduces an asymptotic analysis of the measure for captured trajectories and the behavior of separatrices in nonlinear parametric autoresonance.

Findings

Asymptotic expansion for capture measure

Asymptotic behavior of splitted separatrices

Analysis valid for intermediate small amplitudes

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.