Oscillatory solutions in the planar restricted three-body problem. (English) Zbl 0505.70010
The authors consider the planar restricted problem for large values of the Jacobian constants. Let \(r\) be the distance from the infinitesimal body to the origin, then an oscillatory solution is characterized by \(\limsup_{t\to\infty} r(t)=\infty\) and \(\limsup_{t\to\infty} r(t)<\infty\). The existence of such orbits is proved by the usual method of symbolic dynamics. Furthermore the existence of all possible types of final evolution is proved.
Reviewer: Helmut Rüßmann (Mainz)
MSC:
| 70F07 | Three-body problems |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
Keywords:
planar restricted; large values of Jacobian constant; oscillatory solution; existence; symbolic dynamics; types of final evolutionReferences:
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