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Nonlinear stability of stationary spherically symmetric models in stellar dynamics. (English) Zbl 0727.70015
The author considers a system of particles in the three dimensional space without any collision among them. The system can be described by distribution functions f(x,v,t) satisfying the Vlasov equation and the Poisson law. Then \(f_ 0\), for which \(\partial f/\partial t=0\), is nonlinearly stable under some conditions, and is spherically symmetric if \(f(x,v)=f(Sx,Sv)\) with any rotation S.
The author proves that under an appropriate condition of the state \(f_ 0\), \(f_ 0\) is nonlinearly stable subject to general perturbations and that under a regularity condition, \(f_ 0\) is nonlinearly stable subject to spherically symmetric perturbations.
Reviewer: Y.Kozai (Tokyo)

MSC:
70F15 Celestial mechanics
85A05 Galactic and stellar dynamics
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