2019年7月21日

# Bifurcation of Simó H solution bifurcated from figure-eight choreographies of the equal mass three-body problem

• Hiroshi Fukuda
• ,
• Toshiaki Fujiwara
• ,
• Hiroshi Ozaki

2019年7月20日 - 2019年7月21日

ポスター発表

H solution found by Simó is a periodic orbit of equal mass three bodies which is very close to the famous figure-eight choreography but consists of three distinct orbits. By changing the power a of interaction potential $-1/r^a$ between bodies, the H solution coincides with the figure-eight choreography at a=0.9966. In this study, we calculate numerically the eigenvalue problem on the Hessian operator corresponding to the second variation of the action then investigate the bifurcation of the H solution. The eigenvalues and the eigenfunctions show that 1) the figure-eight choreography bifurcates from/to the H solution at a=0.9966 as above, 2) the H solution annihilates and bifurcates to the orbit with the same symmetry at a=0.816 and a=1.027. 3) Collision in the orbits seems to occur around a=0.9 and a=1.0. This is a joint work with Toshiaki Fujiwara and Hiroshi Ozaki.

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