Oscillatory Escape in a Duffing Equation with a Polynomial Potential

Mark Levi, Jiangong You

Research output: Contribution to journalArticle

11 Citations (Scopus)

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

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Hamiltonians
Duffing Equation
Polynomials
Polynomial
Discontinuity
Infinity
Curve
Invariant

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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title = "Oscillatory Escape in a Duffing Equation with a Polynomial Potential",
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 Poincar{\'e} map possesses no invariant KAM curves enclosing the origin outside a bounded disk.",
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Oscillatory Escape in a Duffing Equation with a Polynomial Potential. / Levi, Mark; You, Jiangong.

In: Journal of Differential Equations, Vol. 140, No. 2, 01.11.1997, p. 415-426.

Research output: Contribution to journalArticle

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AU - Levi, Mark

AU - You, Jiangong

PY - 1997/11/1

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N2 - 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.

AB - 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.

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