JournalsjemsVol. 21, No. 12pp. 3709–3737

Parabolic implosion for endomorphisms of C2\mathbb C^2

  • Fabrizio Bianchi

    Imperial College London, UK, and Université de Lille, Villeneuve-d'Ascq, France
Parabolic implosion for endomorphisms of $\mathbb C^2$ cover
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Abstract

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.

Cite this article

Fabrizio Bianchi, Parabolic implosion for endomorphisms of C2\mathbb C^2. J. Eur. Math. Soc. 21 (2019), no. 12, pp. 3709–3737

DOI 10.4171/JEMS/911