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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.
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Fabrizio Bianchi, Parabolic implosion for endomorphisms of . J. Eur. Math. Soc. 21 (2019), no. 12, pp. 3709–3737DOI 10.4171/JEMS/911