DCDS-S
Random walk in the three-body problem and applications
Edward Belbruno
Discrete & Continuous Dynamical Systems - S 2008, 1(4): 519-540 doi: 10.3934/dcdss.2008.1.519
The process of random walk is described, in general, and how it can be applied in the three-body problem in a systematic manner. Several applications are considered. The main one which is a focus of this paper is on the evolution of horseshoe orbits and their transition to breakout motion in the restricted three-body problem. This connection is related to their use for an Earth-impactor in a theory on the formation of the Moon. We briefly discuss another application on the instability of asteroid orbits.
keywords: horseshoe orbit stability Three-body problem stochastic process bifurcation random walk hyperbolicity collision.

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