Abstract

We study topological bifurcations of classes of spatial central configurations (s.c.c.) from the following highly symmetrical families: two nested regular tetrahedra, octahedra and cubes, two nested rotated regular tetrahedra and two dual regular polyhedra for 14 bodies. We prove the existence of local and global topological bifurcations of s.c.c. from these families. We seek new classes of s.c.c. by using equivariant bifurcation theory. It is worth pointing out that the shapes of the bifurcating families are less symmetrical than the shapes of the considered families of s.c.c.

Highlights

  • One of the most important problems of Celestial Mechanics is the problem of classification of all central configurations (c.c.) in the N -body problem

  • We study topological bifurcations from those families and use the precise formulas for positions and masses provided in the above listed papers of Corbera, Llibre and Pérez-Chavela

  • As in Kowalczyk (2015), we shall address the shapes of the found families of s.c.c. and we prove that the bifurcating families have poorer symmetries or less regular shapes

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Summary

Introduction

One of the most important problems of Celestial Mechanics is the problem of classification of all central configurations (c.c.) in the N -body problem. We apply our abstract results of Kowalczyk (2015) to the spatial N -body problem and we prove the existence of topological bifurcations from the following families of s.c.c.: (2.4), (2.5), (2.6), (2.7) and (2.8).

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