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Parameter spaces in complex dynamics and related topics

Horn maps of semi-parabolic Hénon maps

speaker: Matthieu Astorg (Universite' d'Orléans)

abstract: joint work with Fabrizio Bianchi.

Bedford, Smillie and Ueda have introduced a notion of horn maps for polynomial diffeomorphisms of C² with a semi parabolic fixed points, generalizing classical results from parabolic implosion in one complex variable. We prove that these horn maps satisfy a weak version of the Ahlfors island property. As a consequence, we obtain the density of repelling cycles in their Julia set, and we prove the existence of perturbations of the initial Hénon map for which the forward Julia set J⁺ has Hausdorff dimension arbitrarily close to 4.

timetable:
Thu 30 May, 14:30 - 15:20, Aula Dini
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