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Über die Konstruktion Invarianter Tori, welche von Einer Stationären Grundlösung Eines Reversiblen Dynamischen Systems Abzweigen

  • Jürgen Scheurle
Chapter
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Serie Internationale D’Analyse Numerique book series (ISNM, volume 48)

Abstract

An existence theorem for invariant tori near equilibria of reversible dynamical systems is presented. It is assumed that the linearized vector field has exactly n pairs of simple conjugate eigenvalues moving along the imaginary axis with non-vanishing velocities corresponding to certain external parameters. The remaining part of the spectrum may be arbitrary. The motion on the tori turns out to be quasiperiodic. Finally a generalized Newton method is described which enables one to construct the tori inspite of the arising difficulty with small divisors.

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Literatur

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    Kirchgässner K. und Scheurle J.: On the bounded solutions of a semilinear elliptic equation in a strip, erscheint in J. Diff. Equat.Google Scholar
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Copyright information

© Springer Basel AG 1979

Authors and Affiliations

  • Jürgen Scheurle
    • 1
  1. 1.Math. Institut AUniversität StuttgartStuttgart 80Germany

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