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Vertical bifurcation families from the long and short period families around the equilateral equilibrium points

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Abstract

In this paper, following the increase of the mass ratio μ, the vertical stability curves of the long and the short period families were studied, and the vertical bifurcation families from these two families were computed. It is found that these vertical bifurcation families connect the long and short period families with the spatial periodic family emanating from the equilateral equilibrium points. The evolution details of these vertical bifurcation families were carefully studied and they are found to be similar to the planar bifurcation families connecting the long period family with the short period family in the planar case.

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Authors and Affiliations

  1. Astronomy Department, Nanjing University, Nanjing, 210093, China

    X. Y. Hou & L. Liu

  2. Institute of Space Environment and Astronautics, Nanjing University, Nanjing, 210093, China

    X. Y. Hou & L. Liu

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  1. X. Y. Hou
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  2. L. Liu
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Correspondence to L. Liu.

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Hou, X.Y., Liu, L. Vertical bifurcation families from the long and short period families around the equilateral equilibrium points. Celest Mech Dyn Astr 101, 309–320 (2008). https://doi.org/10.1007/s10569-008-9147-4

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  • DOI: https://doi.org/10.1007/s10569-008-9147-4

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