  We give an estimate of the discontinuity of the large Julia set for a
perturbation of a class of maps tangent to the identity, by means of a
two-dimensional Lavaurs Theorem. We adapt to our situation a strategy due to
Bedford, Smillie and Ueda in the semiattracting setting. We also prove the
discontinuity of the filled Julia set for such perturbations of regular
polynomials.
