Horseshoe periodic orbits with one symmetry in the general planar three-body problem

Abimael Bengochea; Manuel Falconi; Ernesto Pérez-Chavela

doi:10.3934/dcds.2013.33.987

Article Contents

2013, Volume 33, Issue 3: 987-1008. Doi: 10.3934/dcds.2013.33.987

This issue Previous Article Non-integrability criterium for normal variational equations around an integrable subsystem and an example: The Wilberforce spring-pendulum Next Article Variational approach to second species periodic solutions of Poincaré of the 3 body problem

Horseshoe periodic orbits with one symmetry in the general planar three-body problem

1.
Departamento de Matemáticas, Facultad de Ciencias, UNAM, Ciudad Universitaria, México, D.F. 04510
2.
Department of Mathematics, Facultad de Ciencias, UNAM, Ciudad Universitaria, México, D.F. 04510
3.
Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, D.F. 09340

Received: March 31, 2011

Revised: August 31, 2011

Published: February 2013

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Abstract

Using collinear reversible configurations and some properties of symmetry we obtain horseshoe periodic orbits in the general planar three-body problem with masses $m_1\gg m_2 \geq m_3$, which usually represents a system formed by a planet and two small satellites; for instance, the system Saturn-Janus-Epimetheus. For the numerical analysis we have taken the values $m_2/m_1 = 3.5 \times 10^{-4}$ and $m_3/m_1 = 9.7 \times 10^{-5}$ corresponding to $10^5$ times the mass ratios of Saturn-Janus and Saturn-Epimetheus,

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Mathematics Subject Classification: Primary: 70F15, 70F07, 70H12; Secondary: 37M05.

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