Global bifurcations from the center of mass in the Sitnikov problem

Rafael Ortega; Andrés Rivera

doi:10.3934/dcdsb.2010.14.719

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2010, Volume 14, Issue 2: 719-732. Doi: 10.3934/dcdsb.2010.14.719

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Global bifurcations from the center of mass in the Sitnikov problem

Rafael Ortega^1, and
Andrés Rivera^2,

1.
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada
2.
Departamento de Ciencias Naturales y Matemáticas, Facultad de Ingeniería, Pontificia Universidad Javeriana Cali, 26239 Cali

Received: June 2009

Revised: November 2009

Published: September 2010

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Abstract

The Sitnikov problem is a restricted three body problem where the eccentricity of the primaries acts as a parameter. We find families of symmetric periodic solutions bifurcating from the equilibrium at the center of mass. These families admit a global continuation up to excentricity $e=1$. The same techniques are applicable to the families obtained by continuation from the circular problem ($e=0$). They lead to a refinement of a result obtained by J. Llibre and R. Ortega.

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Mathematics Subject Classification: Primary: 70F07; Secondary: 34B15, 37G15, 37N05.

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