Boundedness of Fatou Components of Holomorphic Maps

Cao, Can; Wang, Yuefei

doi:10.1007/s10884-004-2785-7

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Transcendental Entire Functions With No Unbounded Fatou Comp2

Then Every Component Of F (F ) Is Bounded1

Introduction1

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2007

2015

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Cited by 5 publications

(4 citation statements)

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“…However can these results be utilized to get nonexistence of unbounded domains for functions of higher order or even for infinite order? One of the results in this direction is by Cao and Wang [5] who proved the following. N) are nonconstant holomorphic maps each having order less than 1 2 .…”

Section: Then Every Component Of F (F ) Is Boundedmentioning

confidence: 92%

Composite entire functions with no unbounded Fatou components

Singh¹

2007

Journal of Mathematical Analysis and Applications

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Section: Then Every Component Of F (F ) Is Boundedmentioning

confidence: 92%

Composite entire functions with no unbounded Fatou components

Singh¹

2007

Journal of Mathematical Analysis and Applications

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“…Cao and Wang [9] developed a similar result to Corollary 7.2, concerning composition of transcendental entire functions. They showed that if g = f 1 • f 2 • · · · • f k , where f 1 , f 2 , .…”

Section: Transcendental Entire Functions With No Unbounded Fatou Compmentioning

confidence: 66%

“…We note that it is possible to construct a class of log-regular functions of lower order zero and any given finite order, in particular order less than 1 2 . This shows that there are situations in which Corollary 7.2 can be applied but not the result of [9].…”

Section: Transcendental Entire Functions With No Unbounded Fatou Comp...mentioning

confidence: 96%

Entire functions for which the escaping set is a spider's web

Sixsmith¹

2011

Math. Proc. Camb. Phil. Soc.

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Abstract. We construct several new classes of transcendental entire functions, f , such that both the escaping set, I(f ), and the fast escaping set, A(f ), have a structure known as a spider's web. We show that some of these classes have a degree of stability under changes in the function. We show that new examples of functions for which I(f ) and A(f ) are spiders' webs can be constructed by composition, by differentiation, and by integration of existing examples. We use a property of spiders' webs to give new results concerning functions with no unbounded Fatou components.

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“…For Fejér gap, Wang [18] proposed the following problem. Let ( ) be an entire function with Fejér gaps, that is, Cao and Wang [20] proved the following result.…”

Section: Introductionmentioning

confidence: 99%