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

27 Jul 2016  ·  Bianchi Fabrizio ·

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. read more

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Complex Variables Dynamical Systems