  We investigate the collective behaviour of particle orbits in the vicinity of
magnetic reconnection in Earth's magneto-tail. Various regions of different
kinds of orbital stability of particle motions are found. We locate regimes of
temporary capture of particle orbits in configuration space as well as
locations, where strong particle accelerations take place. With this study we
are able to provide a detailed map, i.e. the topology, of high and low
acceleration centers close to the reconnection site. Quasi-regular and chaotic
kinds of motions of elementary particles can be determined as well. The orbital
stability of particle orbits is obtained by a statistical analysis of the
outcome of the system of variational equations of particle orbits within the
framework of particle-in-cell simulations. Using the concept of Lyapunov
Characteristic Numbers to ensembles of particle orbits we introduce Lyapunov
Ensemble Averages to describe the response of particle orbits to local
perturbations induced by the electro-magnetic field.
