arXiv math/06080272006-08math.CVmath.DS

Direct singularities and completely invariant domains of entire functions

Walter Bergweiler, Alexandre Eremenko

备注：: This is the second, corrected version. There were gaps in the proof of the main theorem in the first version
发表信息：: Illinois J. Math. 52 (2008), 243-259

英文摘要：

Let f be a transcendental entire function that omits a complex value a. We show that for every simply connected region D that does not contain a the full preimage of D is disconnected. We conjecture that the same holds if one only assumes that a is omitted locally. We were able to prove this conjecture under the additional assumption that f is of finite order. We include some auxilliary results on the singularities of the inverses of entire functions which are of independent interest.

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