Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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M. Astorg - F. Bianchi

Horn maps of semi-parabolic Hénon maps

created by bianchi on 01 Apr 2024



Inserted: 1 apr 2024
Last Updated: 1 apr 2024

Year: 2024

ArXiv: 2403.20211 PDF


We prove that horn maps associated to quadratic semi-parabolic fixed points of H\'enon maps, first introduced by Bedford, Smillie, and Ueda, satisfy a weak form of the Ahlfors island property. As a consequence, two natural definitions of their Julia set (the non-normality locus of the family of iterates and the closure of the set of the repelling periodic points) coincide. As another consequence, we also prove that there exist small perturbations of semi-parabolic H\'enon maps for which the Hausdorff dimension of the forward Julia set $J^+$ is arbitrarily close to 4.

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