Dynamics of the Restricted Collinear Three-Body Problem
by
Samuel R. Kaplan
University of North Carolina at Asheville
Coauthors: Ernesto A. Lacomba (Universidad Autonoma Metropolitana, Mexico City), Jaume Llibre (Universitat Autonoma de Barcelona, Spain)

We apply symbolic dynamics to continue our previous study of the symmetric collinear restricted three-body problem. Equal mass primaries perform elliptic binary collisions while a third massless body moves in the line between the pimaries between two consecutive elliptic collisions. Based on the existence of a transversal heteroclinic orbit beginning and ending in triple collision hyperbolic equilibria, we prove the existence of a set of itineraries of binary collisions which occur following a directed graph. This settles in the negative an earlier conjecture that for any sequence of natural numbers there is an orbit for which those numbers represent alternatively the number of binary collisions with the left primary or the right one before passing to the other side.

Date received: December 23, 2002