Dynamical system analysis for the Einstein-Yang-Mills equations

Local solutions of the static, spherically symmetric Einstein-Yang-Mills (EYM) equations with SU(2) gauge group are studied on the basis of dynamical systems methods. This approach enables us to classify EYM solutions in the origin neighborhood, to prove the existence of solutions with the oscillating metric as well as the existence of local solutions for all known formal power series expansions, to study the extendibility of solutions, and to find two new local singular solutions.