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 [9] and [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 f44e785899f5b20ca45beca8f5" title="Click to view the MathML source">a<−1$a<-1$.