Permutable entire functions and their Julia sets
نویسندگان
چکیده
منابع مشابه
The Hausdorff Dimension of Julia Sets of Entire Functions Iv
It is known that, for a transcendental entire function f, the Hausdorff dimension of J( f ) satisfies 1% dim J( f )% 2. For each d ` (1, 2), an example of a transcendental entire function f with dim J( f ) ̄ d is given. It is then indicated how this function can be modified to produce a transcendental meromorphic function F with one pole with dim J(F ) ̄ d. These appear to be the first examples o...
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Let f be a transcendental entire function for which the set of critical and asymptotic values is bounded. The Denjoy-Carleman-Ahlfors theorem implies that if the set of all z for which |f(z)| > R has N components for some R > 0, then the order of f is at least N/2. More precisely, we have log logM(r, f) ≥ 1 2 N log r − O(1), where M(r, f) denotes the maximum modulus of f . We show that if f doe...
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We show that if f and g are transcendental entire functions such that f(g) = g(f), then f satisfies an algebraic differential equation if and only if g does.
متن کاملSpiders’ Webs and Locally Connected Julia Sets of Transcendental Entire Functions
We show that, if the Julia set of a transcendental entire function is locally connected, then it takes the form of a spider’s web in the sense defined by Rippon and Stallard. In the opposite direction, we prove that a spider’s web Julia set is always locally connected at a dense subset of buried points. We also show that the set of buried points (the residual Julia set) can be a spider’s web.
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2001
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004101005084