Periodic solutions of continuous self-gravitating systems

  • F. Verhulst
Contributed Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 810)


A collection of self-gravitating particles can be described by the nonlinear system consisting of the collision-less Boltzmann equation and the appropriate Poisson-equation. Such a system can be studied by associating it with dynamical systems in a finite-dimensional phase-space. The finite-dimensional problems are treated in the frame-work of KAM-theory by Birkhoff normalization and averaging techniques. This leads to a classification of possible two-parameter families of periodic solutions in these dynamical systems.

The asymptotic approximations of the solutions in two degrees of freedom problems with a discrete symmetric potential produce ring-type solutions of the original continuous system.


Periodic Solution Resonance Case Stable Periodic Solution General Hamiltonian System Birkhoff Normal Form 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • F. Verhulst
    • 1
  1. 1.Mathematisch InstituutRijksuniversiteit UtrechtUtrechtThe Netherlands

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