Bianchi II magnetic cosmologies

The Einstein-Maxwell field equations for the class of orthogonal Bianchi II cosmologies with a -law perfect fluid and a pure, homogeneous source-free magnetic field are written as an autonomous differential equation in terms of expansion-normalized variables. The future and past asymptotic states for these models are given by the - and -limit sets for the orbits of the resulting dynamical system. These limit sets are studied in detail. As a by-product of the analysis, we find new transitively self-similar solutions to the field equations which act as attractors into the future for a set of models of non-zero measure in this class. The behaviour into the past is described by mixmaster oscillations. Similarities and differences between the asymptotic states of magnetic Bianchi I, II and cosmologies are then discussed from both a mathematical and a physical point of view.