The interplay of dynamical systems analysis and group theory.

Abstract

We investigate the relationship between the Dynamical Systems analysis and the Lie Symmetry analysis of ordinary differential equations. We undertake this investigation by looking at a relativistic model of self-gravitating charged fluids. Specifically we look at the impact of specific parameters obtained from Lie Symmetries analysis on the qualitative behaviour of the model. Steady states, stability and possible bifurcations are explored.