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Global bifurcations from the center of mass in the Sitnikov problem. (English) Zbl 1380.70028

Summary: 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 eccentricity \(e=1\). 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 [SIAM J. Appl. Dyn. Syst. 7, No. 2, 561–576 (2008; Zbl 1159.70010)].

MSC:

70F07 Three-body problems
37N05 Dynamical systems in classical and celestial mechanics
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
70K50 Bifurcations and instability for nonlinear problems in mechanics

Citations:

Zbl 1159.70010
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