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Global bifurcations from the center of mass in the Sitnikov problem

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


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