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Periodic solutions of continuous self-gravitating systems

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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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© 1980 Springer-Verlag

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Verhulst, F. (1980). Periodic solutions of continuous self-gravitating systems. In: Martini, R. (eds) Geometrical Approaches to Differential Equations. Lecture Notes in Mathematics, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089986

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  • DOI: https://doi.org/10.1007/BFb0089986

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10018-8

  • Online ISBN: 978-3-540-38166-2

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