Blowup/scattering alternative for a discrete family of static critical solutions with various number of unstable eigenmodes

Decay of regular static spherically symmetric solutions in the SU(2) Yang-Mills-dilaton (YMd) system of equations under the independent excitation of their unstable eigenmodes has been studied self-consistently in the nonlinear regime. The considered regular YMd solutions form a discrete family and can be parametrised by the number $N=1,2,3,4...$ of their unstable eigenmodes in linear approximation. We have obtained strong numerical evidences in favour of the following statements: i) all static YMd solutions are distinct local threshold configurations, separating blowup and scattering solutions; ii) the main unstable eigenmodes are only those responsible for the blowup/scattering alternative; iii) excitation of higher unstable eigenmodes always leads to finite-time blowup; iv) the decay of the lowest N=1 static YMd solution via excitation of its unique unstable mode is an exceptional case because the resulting waves propagate as a whole without energy dispersion revealing features peculiar to solitons. Applications of the obtained results to Type-I gravitational collapse of massless fields are briefly discussed.