发表机构
East China Normal University（华东师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用双曲面积方法证明了有理映射和一类整函数无游荡Fatou分量，无需拟共形技术，并推广了Sullivan及Eremenko--Lyubich等定理。
AI 中文摘要
在单复变数维度中，我们利用双曲面积证明了次数至少为二的有理映射以及奇异集紧致且所有聚点位于Fatou集中的超越整函数不存在游荡的Fatou分量。作为推论，我们恢复了有理映射的Sullivan定理以及具有有限个奇异值的整函数的Eremenko--Lyubich和Goldberg--Keen定理。该证明既不使用拟共形形变，也不使用Teichmüller理论。
英文摘要
In one complex dimension, we use hyperbolic area to prove the absence of wandering Fatou components for rational maps of degree at least two and for transcendental entire functions whose singular sets are compact and have all their accumulation points in the Fatou set. As corollaries, we recover Sullivan's theorem for rational maps and the theorem of Eremenko--Lyubich and Goldberg--Keen for entire functions with finitely many singular values. The proof uses neither quasiconformal deformation nor Teichmüller theory.
Comments5 pages
