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We exhibit stable finite time blow up regimes for the energy criticalco-rotational Wave Map with the S^2 target in all homotopy classes and for thecritical equivariant SO(4) Yang-Mills problem. We derive sharp asymptotics onthe dynamics at the blow up time and prove quantization of the energy focusedat the singularity.

Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills problems