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Journal of Dynamics and Differential Equations

, Volume 31, Issue 3, pp 1129–1139 | Cite as

Bounding Solutions of a Forced Oscillator

  • Kenneth R. MeyerEmail author
  • Dieter S. Schmidt
Article
  • 113 Downloads

Abstract

We give an alternate proof of a theorem in Wang and You (Z Angew Math Phys 47: 943–952, 1996) which shows that all solutions are bounded for a periodically forced nonlinear oscillator. Our proof relies on constructing an analytic change of variables by a convergent Lie series transformation to simplify the system so that the period map has large invariant curves by Moser’s theorem.

Keywords

Nonlinear oscillator Bounded solutions Invariant curve Twist map 

Mathematics Subject Classification

34C15 34K12 37E40 70H08 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Department of Computer ScienceUniversity of CincinnatiCincinnatiUSA

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