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

详细信息    查看全文

• 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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305583&_mathId=si1.gif&_user=111111111&_pii=S0022247X16305583&_rdoc=1&_issn=0022247X&md5=c558b3616e94fd4f3a66546e6f8efd54" title="Click to view the MathML source">m^⁎class="mathContainer hidden">class="mathCode">$m^{⁎}$. We propose a variation of this problem setting the central mass as the critical value class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305583&_mathId=si1.gif&_user=111111111&_pii=S0022247X16305583&_rdoc=1&_issn=0022247X&md5=c558b3616e94fd4f3a66546e6f8efd54" title="Click to view the MathML source">m^⁎class="mathContainer hidden">class="mathCode">$m^{⁎}$ 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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305583&_mathId=si2.gif&_user=111111111&_pii=S0022247X16305583&_rdoc=1&_issn=0022247X&md5=46a381f44e785899f5b20ca45beca8f5" title="Click to view the MathML source">a<−1class="mathContainer hidden">class="mathCode">$a<-1$.