Abstract
In this paper a description is given of the bifurcation of periodic solutions occurring when a Hamiltonian system of two degrees of freedom passes through nonsemisimple 1∶−1 resonance at an equilibrium. A bifurcation like this is found in the planar circular restricted problem of three bodies at the Lagrange equilibriumL 4 when the mass parameter passes through the critical value of Routh.
Zusammenfassung
Gegenstand dieses Artikels ist die Verzweigung periodischer Lösungen in Hamilton'schen Systemen mit zwei Freiheitsgraden beim Durchgang durch eine nicht-einfache 1∶−1-Resonanz an einem Gleichgewicht. Ein Beispiel ist das ebene restringierte Dreikörperproblem am Lagrange-PunktL 4, wenn die Masse durch den kritischen Wert von Routh hindurchgeht.
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van der Meer, J.C. Bifurcation at nonsemisimple 1∶−1 resonance. Journal of Applied Mathematics and Physics (ZAMP) 37, 425–437 (1986). https://doi.org/10.1007/BF00946761
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DOI: https://doi.org/10.1007/BF00946761