The work of Jorge Ize regarding the n-body problem

Abstract

In this paper we present a summary of the last works of Jorge Ize regarding the global bifurcation of periodic solutions from the equilibria of a satellite attracted by n primary bodies. We present results on the global bifurcation of periodic solutions for the primary bodies from the Maxwell's ring, in the plane and in space, where n identical masses on a regular polygon and one central mass are turning in a plane at a constant speed. The symmetries of the problem are used in order to find the irreducible representations, and with the help of the orthogonal degree theory, all the symmetries of the bifurcating branches. The results presented in this paper were done during the Ph.D. of the author under the direction of Jorge Ize. This paper is dedicated to his memory.