Global bifurcations from the center of mass in the Sitnikov problem

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September 2010, 14(2): 719-732. doi: 10.3934/dcdsb.2010.14.719

Global bifurcations from the center of mass in the Sitnikov problem

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, Colombia

Received June 2009 Revised November 2009 Published June 2010

Abstract
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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.

Keywords: Sitnikov problem, bifurcations, periodic orbits, 3-body problem, global continuation..

Mathematics Subject Classification: Primary: 70F07; Secondary: 34B15, 37G15, 37N0.

Citation: Rafael Ortega, Andrés Rivera. Global bifurcations from the center of mass in the Sitnikov problem. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 719-732. doi: 10.3934/dcdsb.2010.14.719

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