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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Santos, Alan Almeida¹  Marchesin, Marcelo²  Perez-Chavela, Ernesto³  Vidal, Claudio⁴ 

[1] Univ Fed Sergipe, Dept Matemat, Campus Prof Alberto Carvalho, BR-49510200 Itabaiana, SE, Brazil

[2] Univ Fed Minas Gerais, Dept Math, Av Antonio Carlos 6627, BR-31270901 Belo Horizonte, MG, Brazil

[3] ITAM, Dept Math, Calle Rio Hondo 1, Mexico City 01080, DF, Mexico

[4] Univ Bio Bio, Fac Ciencias, Dept Matemat, Casilla 5-C, Concepcion 8, Chile

关键词: N-body problem;    Central configurations;    Dziobek configurations;    Bifurcation;   

DOI  :  10.1016/j.jmaa.2016.09.055

来源: Elsevier

【 摘 要 】

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*. We propose a variation of this problem setting the central mass as the critical value 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free