arXiv Open Access 2024

Horn maps of semi-parabolic Hénon maps

Astorg Matthieu Bianchi Fabrizio

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.DS math.CV

Penulis (2)

Astorg Matthieu

Bianchi Fabrizio

Format Sitasi

APA MLA BibTeX

Matthieu, A., Fabrizio, B. (2024). Horn maps of semi-parabolic Hénon maps. https://arxiv.org/abs/2403.20211

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓