Work

Horn maps of semi-parabolic Hénon maps

Year: 2025

Type: article

Abstract: 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 $$J^+$$ J + is arbitrarily close to 4.

Source: Mathematische Annalen

DOI: 10.1007/s00208-024-03085-3

Authors: Matthieu Astorg, Fabrizio Bianchi

Institutions: Université d'Orléans, Institut Denis Poisson, University of Pisa

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Agence Nationale de la Recherche