Exponentially small splittings of manifolds in a rapidly forced Duffing system

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Abstract

The splitting of the separatrices of the weakly perturbed and rapidly forced Duffing oscillator was examined. Analytic expressions for motions on the perturbed manifolds were first derived, and then asymptotically expanded in series by successive integration by parts. It was shown that the splitting of the manifolds of the rapidly forced problems becomes exponentially small as the perturbation parameter approaches zero. The expression for the splitting distance given by Melnikov theory, is a valid estimate for proving the existence of transverse homoclinic intersections.

Original languageEnglish (US)
Pages (from-to)119-129
Number of pages11
JournalJournal of Sound and Vibration
Volume170
Issue number1
DOIs
StatePublished - Feb 10 1994

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

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