发表机构
School of Mathematics, Nanjing University（南京大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明谢尔宾斯基地毯参数在有限型超越整函数族的双曲分支点集中稠密，并构造了具有此类 Julia 集且含吸引盆、抛物盆、Siegel 盘或游荡域的具体函数。
AI 中文摘要
我们证明了谢尔宾斯基地毯参数在具有恰好一条活跃临界轨道的有限型超越整函数的某些自然族的双曲分支点集中是稠密的。此外，我们构造了一些具有谢尔宾斯基地毯 Julia 集的特定超越整函数，使得它们包含吸引盆、抛物盆、Siegel 盘或游荡域。证明主要基于应用多项式类重整化以及先前获得的关于超越 Julia 集局部连通性的一些结果。
英文摘要
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.
Comments20 pages, 4 figures
