Permutable entire functions and multiply connected 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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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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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2016
ISSN: 0001-8708
DOI: 10.1016/j.aim.2015.04.031