Periodic solutions with alternating singularities in the collinear four-body problem |
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Authors: | Tiancheng Ouyang Duokui Yan |
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Affiliation: | 1.Department of Mathematics,Brigham Young University,Provo,USA;2.Chern Institute of Mathematics, Nankai University,Tianjin,People’s Republic of China |
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Abstract: | This paper gives an analytic proof of the existence of Schubart-like orbit, a periodic orbit with singularities in the symmetric collinear four-body problem. In each period of the Schubart-like orbit, there is a binary collision (BC) between the inner two bodies and a simultaneous binary collision (SBC) of the two clusters on both sides of the origin. The system is regularized and the existence is proved by using a “turning point” technique and a continuity argument on differential equations of the regularized Hamiltonian. |
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