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Connectedness properties of julia sets of transcendental entire functions

 

作者: P. Domínguez,  

 

期刊: Complex Variables, Theory and Application: An International Journal  （Taylor Available online 1997）
卷期: Volume 32, issue 3  

页码: 199-215

 

ISSN:0278-1077

 

年代: 1997

 

DOI:10.1080/17476939708814991

 

出版商: Gordon and Breach Science Publishers

 

关键词: Julia set;entire function;periodic cycle;buried component;Classification Categories: AMS subject classification 30D05;58F08

 

数据来源: Taylor

 

摘要:

For a transcendental entire functionfwe investigate the connectedness properties of the Julia setJ(f) in the plane and in the Riemann sphere. We give examples whereJ(f) contains buried components, that is, components which do not meet the boundary of any component of the complementF(f) ofJf). In connection with an old question of Fatou we show that ifFfhas a multiply-connected component, thenJfhas buried components which arc singletons. Such components are dense inJf).

 

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