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PreprintarXiv licencearXiv

Sierpiński carpet Julia sets of transcendental entire functions

  • Weiwei Su
  • Fei Yang
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Abstract

We prove that Sierpiński carpet parameters are dense in the bifurcation loci of some natural families of finite type transcendental entire functions having exactly one active critical orbit. Moreover, some specific transcendental entire functions with Sierpiński carpet Julia sets are constructed such that they contain either an attracting basin, a parabolic basin, a Siegel disk or wandering domains. The proofs are mainly based on applying the polynomial-like renormalization and some results on the local connectivity of transcendental Julia sets obtained before.

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Cite

BibTeXRIS
BibTeX
@misc{su2026sierpiński,
  title = {{Sierpiński carpet Julia sets of transcendental entire functions}},
  author = {Weiwei Su and Fei Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22740},
  eprint = {2609.22740},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22740},
}
RIS
TY  - UNPB
TI  - Sierpiński carpet Julia sets of transcendental entire functions
AU  - Weiwei Su
AU  - Fei Yang
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22740
UR  - https://arxiv.org/abs/2609.22740
AB  - We prove that Sierpiński carpet parameters are dense in the bifurcation loci of some natural families of finite type transcendental entire functions having exactly one active critical orbit. Moreover, some specific transcendental entire functions with Sierpiński carpet Julia sets are constructed such that they contain either an attracting basin, a parabolic basin, a Siegel disk or wandering domains. The proofs are mainly based on applying the polynomial-like renormalization and some results on the local connectivity of transcendental Julia sets obtained before.
ER  -