@inproceedings{7261c1231f324b718330815ace714604,
title = "Splitting of separatrices in the rapidly forced Duffing oscillator",
abstract = "The splitting of the stable and unstable manifolds of the rapidly forced Duffing oscillator with negative stiffness is investigated. The method used relies on the computation of analytic approximations for the orbits on the perturbed manifolds, and the asymptotic approximation of these orbits by successive integrations by parts. It is shown, that the splitting of the manifolds becomes exponentially small as the perturbation parameter tends to zero, and that the estimate for the splitting distance given by the Melnikov Integral dominates over high order corrections.",
author = "Vakakis, {Alexander F.}",
year = "1993",
language = "English (US)",
isbn = "0791811719",
series = "American Society of Mechanical Engineers, Design Engineering Division (Publication) DE",
publisher = "Publ by ASME",
pages = "249--255",
editor = "Mo Shahinpoor and H.S. Tzou",
booktitle = "Nonlinear Vibrations",
note = "14th Biennial Conference on Mechanical Vibration and Noise ; Conference date: 19-09-1993 Through 22-09-1993",
}