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.
Citation: Samuel R. Kaplan, Ernesto A. Lacomba, Jaume Llibre. Symbolic dynamics of the elliptic rectilinear restricted 3--body problem. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 541-555. doi: 10.3934/dcdss.2008.1.541
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