• Corpus ID: 211068711

Variational principle of action and group theory for bifurcation of figure-eight solutions

  title={Variational principle of action and group theory for bifurcation of figure-eight solutions},
  author={Toshiaki Fujiwara and Hiroshi Fukuda and Hiroshi Ozaki},
  journal={arXiv: Mathematical Physics},
Figure-eight solutions are solutions to planar equal mass three-body problem under homogeneous or inhomogeneous potentials. They are known to be invariant under the transformation group $D_6$: the dihedral group of regular hexagons. Numerical investigation shows that each figure-eight solution has some bifurcation points. Six bifurcation patterns are known with respect to the symmetry of the bifurcated solution. In this paper we will show the followings. The variational principle of action and… 

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