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

Samuel R. Kaplan; Ernesto A. Lacomba; Jaume Llibre

doi:10.3934/dcdss.2008.1.541

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2008, Volume 1, Issue 4: 541-555. Doi: 10.3934/dcdss.2008.1.541

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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
2.
Departamento de Matemáticas, Universidad Autónoma Metropolitana–Iztapalapa, Av. San Rafael Atlixco 186, C.P. 09340 México, D.F.
3.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona

Received: January 2006

Revised: July 2008

Published: December 2008

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Abstract

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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Mathematics Subject Classification: Primary: 70F07; Secondary: 70F15.

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