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Theory of Newtonian self-gravitating stationary spherically symmetric systems

Published online by Cambridge University Press:  11 January 2006

J. MARK HEINZLE ,
ALAN D. RENDALL  and
CLAES UGGLA
J. MARK HEINZLE
Affiliation:
Max-Planck-Institut für Gravitationsphysik, Albert–Einstein–Institut Am Mühlenberg 1, D-14476 Golm, Germany. e-mail: Mark.Heinzle@aei.mpg.deAlan.Rendall@aei.mpg.de
ALAN D. RENDALL
Affiliation:
Max-Planck-Institut für Gravitationsphysik, Albert–Einstein–Institut Am Mühlenberg 1, D-14476 Golm, Germany. e-mail: Mark.Heinzle@aei.mpg.deAlan.Rendall@aei.mpg.de
CLAES UGGLA
Affiliation:
Department of Physics, University of Karlstad, S-651 88 Karlstad, Sweden. e-mail: Claes.Uggla@kau.se
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Abstract

We investigate spherically symmetric equilibrium states of the Vlasov–Poisson system, relevant in galactic dynamics. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations on a region with compact closure. Based on a dynamical systems analysis we derive theorems that guarantee that the steady state solutions have finite mass and compact support.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 140 , Issue 1 , January 2006 , pp. 177 - 192
Copyright
2006 Cambridge Philosophical Society

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