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Periodic solutions of continuous self-gravitating systems

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

Abstract

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.

Keywords

Periodic Solution Resonance Case Stable Periodic Solution General Hamiltonian System Birkhoff Normal Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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