Absence of line fields and Mane's theorem for nonrecurrent transcendental functions
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 0002-9947Full text not available from this repository.
Official URL: http://dx.doi.org/10.1090/S0002-9947-2010-05125-6
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|
|Official Date:||January 2011|
|Number of Pages:||26|
|Page Range:||pp. 203-228|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC)|
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