Periodic solutions of continuous self-gravitating systems
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.
KeywordsPeriodic Solution Resonance Case Stable Periodic Solution General Hamiltonian System Birkhoff Normal Form
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