A new analysis of the three-body problem

Abstract

Intherecentpapers[5,18],respectively,theexistenceofmotionswhere the perihelions afford periodic oscillations about certain equilibria and the onset of a topological horseshoe have been proved. Such results have been obtained using, as neighbouring integrable system, the so-called two-centre (or Euler) problem and a suitable canonical setting proposed in [16, 17]. Here we review such results.