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Linear Ordinary Differential Equations with Quasiperiodic Coefficients

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

Abstract

In this section we wish to study the general form of the solution matrix Q(t) of the differential equation
$$ \dot Q\left( t \right) = M\left( t \right)Q\left( t \right) $$
(3.1.1)
where M is a complex-valued m × m matrix which can be expressed as a Fourier series of the form
$$ M\left( t \right) = \sum\limits_{n1,n2, \ldots ,nN} {M_{n1,n2, \ldots ,nN} \exp } \left( {{\text{i}}\omega _1 n_1 t + {\text{i}}\omega _N n_N t} \right). $$
(3.1.2)
.

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Bibliography

  1. H. Haken: Z. Naturforsch. 8A, 228 (1954)ADSGoogle Scholar
  2. H. Haken: In Dynamics of Synergetic Systems, Springer Ser. Synergetics, Vol. 6, ed. by H. Haken (Springer, Berlin, Heidelberg, New York 1980) p. 16Google Scholar
  3. For the proof of Theorem 3.8.2 I used auxiliary theorems represented in N. Dunford, J. T. Schwartz: Linear Operators, Pure and Applied Mathematics, Vol. VII, Parts I-III (Wiley, Interscience, New York 1957)Google Scholar
  4. N. N. Bogoliubov, I. A. Mitropolskii, A. M. Samoilento: Methods of Accelerated Convergence in Google Scholar
  5. Nonlinear Mechanics (Springer, Berlin, Heidelberg, New York 1976)Google Scholar
  6. The results of Sect. 3.9 are taken from N. N. Bogoliubov, I. A. Mitropolskii, A. M. Samoilento I.c.Google 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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