Ergodic Theory and Dynamical Systems

Research Article

Relative equilibria of the four-body problem

Richard Moeckela1

a1 School of Mathematics, University of Minnesota-Twin Cities, Minneapolis, MN 55455, USA

Abstract

By employing a regularizing transformation, the problem of bifurcation of relative equilibria in the Newtonian 4-body problem is reduced to a study of an algebraic correspondence between real algebraic varieties. The finiteness theorems of algebraic geometry are used to find an upper bound for the number of affine equivalence classes of relative equilibria which holds for all masses in the complement of a proper, algebraic subset of the space of all masses.

(Received October 10 1984)

(Revised February 25 1984)