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Existence of wandering and periodic domain in given angular region. (English) Zbl 1482.30074

Summary: Dynamics of composition of entire functions is well related to it’s factors, as it is known that for entire functions \(f\) and \(g\), \(f\circ g\) has wandering domain if and only if \(g\circ f\) has wandering domain. However the Fatou components may have different structures and properties. In this paper we have shown the existence of domains with all possibilities of wandering and periodic in given angular region \(\theta\).

MSC:

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
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References:

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