Continuation and bifurcations of concave central configurations in the four and five body-problems for homogeneous force laws

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• 作者：Alan Almeida Santos^a ; ^{alan@ufs.br" class="auth_mail" title="E-mail the corresponding author} ; Marcelo Marchesin^b ; ^{mdm@mat.ufmg.br" class="auth_mail" title="E-mail the corresponding author} ; Ernesto Pé ; rez-Chavela^c ; ¹ ; ^{epc@xanum.uam.mx" class="auth_mail" title="E-mail the corresponding author} ; Claudio Vidal^d ; ^{clvidal@ubiobio.cl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：N-body problem ; Central configurations ; Dziobek configurations ; Bifurcation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1743-1768
• 全文大小：586 K

文摘

The central configurations given by an equilateral triangle and a regular tetrahedron with equal masses at the vertices and a body at the barycenter have been widely studied in br0010">[9] and br0020">[14] due to the phenomena of bifurcation occurring when the central mass has a determined value m^⁎$m^{⁎}$. We propose a variation of this problem setting the central mass as the critical value m^⁎$m^{⁎}$ and letting a mass at a vertex to be the parameter of bifurcation. In both cases, 2D and 3D, we verify the existence of bifurcation, that is, for a same set of masses we determine two new central configurations. The computation of the bifurcations, as well as their pictures have been performed considering homogeneous force laws with exponent a<−1$a<-1$.