AI 中文总结
本文针对有理映射的无限连通抛物型法图域，证明简单抛物映射可作为其全纯模型，且此类映射可被扰动为带完全不变吸引法图域的有理映射，不改变朱利亚集拓扑，证实了Goldberg–Milnor猜想。
AI 中文摘要
本文是关于有理映射的无限连通抛物型法图域全纯模型问题的后续研究。我们证明了简单抛物映射可作为此类抛物型法图域的全纯模型。此外，我们表明每个简单抛物映射都可被扰动为具有完全不变吸引法图域的有理映射，且不改变朱利亚集的拓扑，从而证实了简单抛物映射的Goldberg–Milnor猜想。
英文摘要
We prove that two simple parabolic rational maps with conformally conjugate completely invariant parabolic Fatou domains are globally conformally conjugate. The proof combines quasiconformal rigidity with the absence of invariant line fields for simple parabolic maps. Together with our previous existence theorem, the rigidity result gives existence and uniqueness of simple parabolic models for infinitely-connected fixed parabolic Fatou domains. We further obtain a rational-map analogue of the Goldberg--Milnor perturbation conjecture.
Comments33 pages, 4 figures
