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On the Sitnikov problem. (English) Zbl 0718.70005

Summary: A mapping which reflects the properties of the Sitnikov problem is derived. We study the mapping instead of the original differential equations and discover that there exists a hyperbolic invariant set. The theoretical prediction of the disorder region agrees remarkably with numerical results. We also discuss the LCEs and KS-entropy of the dynamical system.

MSC:

70F15 Celestial mechanics
37-XX Dynamical systems and ergodic theory
70-08 Computational methods for problems pertaining to mechanics of particles and systems
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