We study Wave Maps from R^{ 2+1} to the hyperbolic plane with smooth compactly supported initial data which are close to smooth spherically symmetric ones with respect to some H^{ 1+\mu}, \mu>0. We show that such Wave Maps don't develop singularities and stay close to the Wave Map extending the spherically symmetric data with respect to all H^{ 1+\delta}, \delta<\mu_{ 0}(\mu). We obtain a similar result for Wave Maps whose initial data are close to geodesic ones. This generalizes a theorem of Sideris for this context.
Categories: math.AP