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Qualitative Theory of Nonlinear Resonance by Averaging and Dynamical Systems Methods

  • James Murdock
Chapter
Part of the Dynamics Reported book series (DYNAMICS, volume 1)

Abstract

This paper is a self-contained exposition of the theory of averaging for periodic and quasiperiodic systems, with the emphasis being on the author’s research (part of it joint work with Clark Robinson) on qualitative aspects of nonlinear resonance. Many topics in averaging theory are not covered, among them: averaging for systems more general than quasiperiodic; relations between averaging and multiple time-scale methods; Eckhaus’s approach to averaging; combinations of averaging with matching of asymptotic expansions. The principal question which is addressed is: when does averaging (to first or higher order) lead to an accurate qualitative description of the solutions of the original (unaveraged) equation? By qualitative description we mean both locally (existence and stability of certain invariant sets such as periodic orbits, or almost invariant ‘lingering’ and globally (connecting orbits between invariant sets, or claims that in certain large regions all orbits drift in a certain direction).

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Copyright information

© John Wiley & Sons and B. G. Teubner 1988

Authors and Affiliations

  • James Murdock
    • 1
  1. 1.Department of MathematicsIowa State UniversityUSA

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