2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74372We 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+μ}, μ>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+δ}, δ<μ_{0}(μ). 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.78 pagesAnalysis of PDEs35L05text