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

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


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.


Local Coordinate System Iteration Procedure Adiabatic Approximation Nonlinear Coupling Quasiperiodic Solution 
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  3. J. Moser: Math. Ann. 169, 136 (1967)zbMATHCrossRefMathSciNetGoogle Scholar
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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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