Global bifurcations from the center of mass in the Sitnikov problem
Rafael Ortega - Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain (email)
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.
Keywords: 3-body problem, Sitnikov problem, periodic orbits,bifurcations, global continuation.
Received: June 2009; Revised: November 2009; Published: June 2010.
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