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arXiv · 1607.08104

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

Fabrizio Bianchi
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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.

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Fabrizio Bianchi. 2016-07-27. Parabolic implosion for endomorphisms of $\mathbb{C}^2$. https://arxiv.org/abs/1607.08104

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