On the Dynamics and Topology of the Elliptic Rectilinear Restricted 3-Body Problem

Author: Lacomba Ernesto   Llibre Jaume  

Publisher: Springer Publishing Company

ISSN: 0923-2958

Source: Celestial Mechanics and Dynamical Astronomy, Vol.77, Iss.1, 2000-05, pp. : 1-15

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Abstract

We study a symmetric collinear restricted 3-body problem, where the equal mass primaries perform elliptic collisions, while a third massless body moves in the line between the primaries, during the time between two consecutive elliptic collisions. After desingularizing binary and triple collisions, we prove the existence of a transversal heteroclinic orbit beginning and ending in triple collision. This orbit is the unique homothetic orbit that the problem possess. Finally, we describe the topology of the compact extended phase space.