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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

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, Colombia

Received  June 2009 Revised  November 2009 Published  June 2010

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 and Continuous Dynamical Systems - B, 2010, 14 (2) : 719-732. doi: 10.3934/dcdsb.2010.14.719
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