Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Random walk in the three-body problem and applications

Pages: 519 - 540, Volume 1, Issue 4, December 2008      doi:10.3934/dcdss.2008.1.519

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Edward Belbruno - Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, United States (email)

Abstract: 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:  Three-body problem, random walk, horseshoe orbit, bifurcation, stability, stochastic process, hyperbolicity, collision.
Mathematics Subject Classification:  Primary: 37N05, 60G35, 70F05, Secondary: 37M05, 37M20,37J20, 37J25.

Received: April 2008;      Revised: July 2008;      Available Online: September 2008.