# American Institute of Mathematical Sciences

December  2008, 1(4): 541-555. doi: 10.3934/dcdss.2008.1.541

## Symbolic dynamics of the elliptic rectilinear restricted 3--body problem

 1 Department of Mathematics, University of North Carolina Asheville, CPO#2350 Asheville, NC 28804-8511, United States 2 Departamento de Matemáticas, Universidad Autónoma Metropolitana–Iztapalapa, Av. San Rafael Atlixco 186, C.P. 09340 México, D.F., Mexico 3 Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona

Received  January 2006 Revised  July 2008 Published  September 2008

We apply symbolic dynamics to continue our previous study of 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. Based on properties of the homothetic orbit, which is a transversal heteroclinic orbit beginning and ending in triple collision hyperbolic equilibria and using a global Poincaré section, we describe the possible itineraries of binary collisions an orbit can have.
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