  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.
