Bifurcations of Central Configurations in the Four-Body Problem with some equal masses

Abstract

We study the bifurcations of central configurations of the Newtonian four-body problem when some of the masses are equal. First, we continue numerically the solutions for the equal mass case, and we find values of the mass parameter at which the number of solutions changes. Then, using the Krawczyk method and some result of equivariant bifurcation theory, we rigorously prove the existence of such bifurcations and classify them.

References in corpus (4)

• Some Problems on the Classical N-Body Problem
• Symmetry of Planar Four-Body Convex Central Configurations
• Convex Four Body Central Configurations with Some Equal Masses
• Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

Cited by in corpus (5)

• Chebyshev-Taylor parameterization of stable/unstable manifolds for periodic orbits: implementation and applications
• Four-body central configurations with one pair of opposite sides parallel
• Symmetric Central Configurations in the Concave 4-Body Problem with Two Pairs of Equal Masses
• Symmetric relative equilibria with one dominant and four infinitesimal point vortices
• Planar $N$-body central configurations with a homogeneous potential