Oscillatory Escape in a Duffing Equation with a Polynomial Potential

Mark Levi, Jiangong You

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We show that the time-periodic Hamiltonian systemsd2x/dt2+x2n+1+a(t)x2l+1=0, 2n>2l>n, with a discontinuity ina(t), possess unbounded solutionsx(t) which, moreover, oscillate between a finite disk and infinity; in particular liminft→∞x(t)<∞ and limsupt→∞x(t)=∞. As a consequence, the Poincaré map possesses no invariant KAM curves enclosing the origin outside a bounded disk.

Original languageEnglish (US)
Pages (from-to)415-426
Number of pages12
JournalJournal of Differential Equations
Volume140
Issue number2
DOIs
StatePublished - Nov 1 1997

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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