中文

Simultaneous Approximation by Attracting Basins

动力系统 2026-05-12 v1 复变函数

摘要

We show that any d3d\geq3 pairwise-disjoint open sets A1A_1, ..., AdC^A_d\subset\widehat{\mathbb{C}} sharing a common boundary JJ can be simultaneously approximated by the dd attracting basins A1\mathcal{A}_1, ..., Ad\mathcal{A}_d of a rational map rr having Fatou set F(r)=A1...Ad\mathcal{F}(r)=\mathcal{A}_1\sqcup...\sqcup\mathcal{A}_d and so that the Julia set J(r)\mathcal{J}(r) approximates JJ.

引用

@article{arxiv.2605.09903,
  title  = {Simultaneous Approximation by Attracting Basins},
  author = {Colton Fisher and Aiden Hill and Kirill Lazebnik and Palmer Thompson},
  journal= {arXiv preprint arXiv:2605.09903},
  year   = {2026}
}