Resonances in a continuously forced anharmonic oscillator

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Abstract

Periodically forced motion of a classical particle in a one-dimensional potential with superquadratic growth at infinity is considered. It is shown that an arbitrary amount of energy can be transmitted to the oscillator by exciting the system with a continuous time-periodic forcing. This result extends Littlewood's example of unbounded motions in the presence of a discontinuous periodic forcing and, thus, sheds light on the relation between the smoothness of forcing and the stability of motion. A new version of the averaging procedure, which had to be applied to justify the construction, is outlined.

Original languageEnglish (US)
Pages (from-to)264-270
Number of pages7
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume224
Issue number4-5
DOIs
StatePublished - Jan 13 1997
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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