Iteration of Rational Functions
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Cites background or methods from "Iteration of Rational Functions"
...component [82], essentially parabolic domain [24], and domains at ∞ [59] are also used. The term “Baker domain” seems to have been used first in [69, 70]. Besides the papers cited already, we refer to [27, 108, 127] for a proof of the classification theorem. Here only the case that f is rational is considered, but the changes necessary to handle the case that f is transcendental are minor. We note that if f is en...
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...osely speaking—a contradiction is obtained from the fact that there are many quasiconformal homeomorphisms of U n0 and hence many functions µ but not so many functions fΦ. For the details we refer to [16, 24, 27]. In case (ii) it is not difficult to obtain a contradiction to Theorem 10 if f is entire and contained in S, F, or N. A result similar to Theorem 10 can still be obtained if f has finitely many poles, a...
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...cent years work on the iteration of transcendental meromorphic functions has also begun. There exist a number of introductions to and surveys of the iteration theory of rational functions. We mention [27, 37, 42, 53, 63, 69, 93, 100, 108, 128] among the more recent ones but also some older ones [40, 46, 110]. There are comparatively few expositions of the iteration theory of transcendental functions. We refer to [18] for the iteration of e...
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Cites background from "Iteration of Rational Functions"
...(In [ 1 ] as well as in [3, 24] only the case of rational functions is discussed, in which case only critical values need to be considered, but the proof extends to the transcendental case, if we also take asymptotic values into account.) Since f has innitely many multiple zeros and since Leau domains related to distinct xed points of g are disjoint, we deduce that the set of critical and asymptotic values of g is innite....
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...Theorem 1 and its corollaries may be useful in many questions involving meromorphic functions of nite order, in particular in the iteration theory of rational [ 1 , 3, 24] and transcendental meromorphic [2] functions....
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