scholarly journals On the uniform perfectness of diffeomorphism groups

2019 ◽  
Author(s):  
Takashi Tsuboi
Keyword(s):  
Diffeomorphism Groups ◽  
Uniform Perfectness

On uniformly perfect boundary of stable domains in iteration of meromorphic functions II

2002 ◽  
Vol 132 (3) ◽  
pp. 531-544 ◽  
Author(s):  
ZHENG JIAN-HUA
Keyword(s):  
Entire Function ◽  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Julia Set ◽  
Fatou Set ◽  
Deficient Value ◽  
Uniformly Perfect ◽  
Simply Connected ◽  
Stable Domains ◽  
Uniform Perfectness

We investigate uniform perfectness of the Julia set of a transcendental meromorphic function with finitely many poles and prove that the Julia set of such a meromorphic function is not uniformly perfect if it has only bounded components. The Julia set of an entire function is uniformly perfect if and only if the Julia set including infinity is connected and every component of the Fatou set is simply connected. Furthermore if an entire function has a finite deficient value in the sense of Nevanlinna, then it has no multiply connected stable domains. Finally, we give some examples of meromorphic functions with uniformly perfect Julia sets.

On isomorphic classical diffeomorphism groups, III

1995 ◽  
Vol 13 (2) ◽  
pp. 117-127 ◽  
Author(s):  
Augustin Banyaga ◽  
Andrew McInerney
Keyword(s):  
Diffeomorphism Groups
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