非回归超越函数的线场缺失与Mane定理
Absence of line fields and Mane's theorem for non-recurrent transcendental functions
摘要：
设f是超越亚纯函数。设f的后奇异集的有限部分是有界的，f没有常返临界点和游荡域，且f的前极点的次数是一致有界的.证明了f在其朱利亚集上不支持不变线域.我们证明了这一点，通过推广两个结果约有理函数的超越设置：一个定理的Mane关于分支的迭代原像的磁盘，和一个定理的McMullen关于不存在不变的线字段的“可测传递”的功能。这两个定理都推广了Graczyk、Kotus和Swiatek的结果。
英文摘要：
Let f be a transcendental meromorphic function. Suppose that the finite part of the postsingular set of f is bounded, that f has no recurrent critical points or wandering domains, and that the degree of pre-poles of f is uniformly bounded. Then we show that f supports no invariant line fields on its Julia set. We prove this by generalizing two results about rational functions to the transcendental setting: a theorem of Mane about the branching of iterated preimages of disks, and a theorem of McMullen regarding absence of invariant line fields for "measurably transitive" functions. Both our theorems extend results previously obtained by Graczyk, Kotus and Swiatek.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
