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Nonlinear Coupling of Oscillators: The Case of Persistence of Quasiperiodic Motion

  • Hermann Haken
Chapter
Part of the Springer Series in Synergetics book series (SSSYN, volume 20)

Abstract

In this chapter we shall present a theorem developed by Moser which extends former work by Kolmogorov and Arnold. The problem to be treated contains those of Sects. 3.9 and 5.2, 3 as special cases. As we have seen before, a set of linearly coupled harmonic oscillators can oscillate at certain basic frequencies so that their total motion is a special case of a quasiperiodic motion. In this chapter we shall deal with the important problem whether nonlinearly coupled oscillators can also perform quasiperiodic motion. We also include in this consideration oscillators which by themselves are nonlinear.

Keywords

Local Coordinate System Iteration Procedure Adiabatic Approximation Nonlinear Coupling Quasiperiodic Solution 
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Bibliography

  1. A. N. Kolmogorov: Dokl. Akad. Nauk. USSR 98, 527 (1954)zbMATHMathSciNetGoogle Scholar
  2. V. I. Arnol’d: Russ. Math. Surv. 18, 9 (1963)CrossRefGoogle Scholar
  3. J. Moser: Math. Ann. 169, 136 (1967)zbMATHCrossRefMathSciNetGoogle Scholar
  4. J. Moser: “Nearly Integrable and Integrable Systems”, in Topics in Nonlinear Dynamics, ed. by S. Jorna (AIP Conf. Proc. 46, 1 1978)ADSGoogle Scholar
  5. M. V. Berry: “Regular and Irregular Motion”, in Topics in Nonlinear Dynamics, ed. by S. Jorna (AIP Conf. Proc. 46, 16 1978)ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Hermann Haken
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

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