Rempe, Lasse and van Strien, Sebastian. (2011) Absence of line fields and Mane's theorem for nonrecurrent transcendental functions. Transactions of the American Mathematical Society, Vol.363 (No.1). pp. 203-228. ISSN 0002-9947

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Abstract

Let f : C -> (C) over cap be a transcendental meromorphic function. Suppose that the finite part P(f)boolean AND C 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 (1993) about the branching of iterated preimages of disks, and a theorem of McMullen (1994) regarding the absence of invariant line fields for "measurably transitive" functions. Both our theorems extend results previously obtained by Graczyk, Kotus and Swiatek (2004).

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Transactions of the American Mathematical Society
Publisher:	American Mathematical Society
ISSN:	0002-9947
Date:	January 2011
Volume:	Vol.363
Number:	No.1
Number of Pages:	26
Page Range:	pp. 203-228
Identification Number:	10.1090/S0002-9947-2010-05125-6
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/E017886/1
URI:	http://wrap.warwick.ac.uk/id/eprint/4607

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