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
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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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