An entire function which has wandering domains
نویسندگان
چکیده
منابع مشابه
An Entire Function with Simply and Multiply Connected Wandering Domains
We modify a construction of Kisaka and Shishikura to show that there exists an entire function f which has both a simply connected and a multiply connected wandering domain. Moreover, these domains are contained in the set A(f) consisting of the points where the iterates of f tend to infinity fast. The results answer questions by Rippon and Stallard.
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If p is entire, g(z) = a + b exp(2i=c), where a , b , c are non-zero constants and the normal set of g(p) has no wandering components, then the same is true for the normal set of p(g). Let f be a rational function of degree at least 2 or a nonlinear entire function. Let f n , for n 2 N denote the nth iterate of f. Denote the set of normality by N(f) and the Julia set by J(f). Thus N(f) = fz : (...
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N(f) is the 'set of normality' and J(f) is the 'Fatou-Julia' set for / . By definition, N(f) is open (possibly empty). It is easily shown (see, for example, [6,7]) that J(f) is non-empty and perfect, and, further, that J{f) is completely invariant under mapping by / , by which is meant that z e J(f) implies both /(z) e J(f) and c e J(f) for any c which satisfies f(c) = z. Also N(f) is completel...
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If p is entire, g(z) = a+ b exp(2πi/c) , where a , b , c are non-zero constants and the normal set of g(p) has no wandering components, then the same is true for the normal set of p(g) . Let f be a rational function of degree at least 2 or a nonlinear entire function. Let f , for n ∈ N denote the nth iterate of f . Denote the set of normality by N(f) and the Julia set by J(f) . Thus N(f) = {z :...
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Let f (z) be an entire function and M(r) the maximum of I f (z) on z = r . We give some results on the density of the set of points at which f (z) I is small in comparison with M(r) ; although simple, these results seem not to have been noticed before . If E is a measurable set in the z-plane, we denote by DR (E) the ratio m(z c E, I z < R)/1rRZ and by D(E) and D(E) the upper and lower densitie...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1976
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700015287