Analyzing the circular restricted three body problem by set oriented numerical methods

Professor Oliver Junge, Department of Mathematics and Computer Science, University of Paderborn, Germany

Recently, efficient set oriented numerical methods have been developed for the numerical analysis of dynamical systems. These methods allow for the approximation of general invariant sets of arbitrary topology and of invariant manifolds of (in principle) arbitrary dimension. They are based on adaptive multilevel subdivision strategies that compute a tight box-covering of the set of interest. Based on this, statistical information about the dynamics like natural invariant measures and almost invariant sets can easily be computed.

In this talk we show how to adapt these methods to the Hamiltonian context and use the resulting algorithm to compute a covering of part of the two-dimensional global unstable manifold of an unstable periodic orbit in the circular restricted three body problem. We outline why the set oriented methods can provide an efficient way of finding connecting orbits between arbitrary invariant sets. This will be illustrated by several examples, including the planar circular restricted three body problem.