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Pré-Publication, Document De Travail Année : 2024

Horn maps of semi-parabolic Hénon maps

Matthieu Astorg
Fabrizio Bianchi

Résumé

We prove that horn maps associated to quadratic semi-parabolic fixed points of Hénon 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 Hénon maps for which the Hausdorff dimension of the forward Julia set J+ is arbitrarily close to 4.
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Dates et versions

hal-04526813 , version 1 (29-03-2024)

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  • HAL Id : hal-04526813 , version 1

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Matthieu Astorg, Fabrizio Bianchi. Horn maps of semi-parabolic Hénon maps. 2024. ⟨hal-04526813⟩
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