Parabolic implosion for endomorphisms of $\mathbb C^2$

Fabrizio Bianchi (1, 2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 CNRS - Centre National de la Recherche Scientifique

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.

Domaines: Mathématiques [math]

Fabrizio Bianchi. Parabolic implosion for endomorphisms of $\mathbb C^2$. Journal of the European Mathematical Society, 2019, 21 (12), pp.3709-3737. ⟨10.4171/JEMS/911⟩. ⟨hal-03039606⟩