The phase space structure around L-4 in the restricted three-body problem

The phase space structure around L-4 in the restricted three-body problem i s investigated. The connection between the long period family emanating fro m L-4 and the very complex structure of the stability region is shown by us ing the method of Poincare's surface of section. The zero initial velocity stability region around L-4 is determined by using a method based on the ca lculation of finite-time Lyapunov characteristic numbers. It is shown that the boundary of the stability region in the configuration space is formed b y orbits suffering slow chaotic diffusion.