scholarly journals On the uniform perfectness of groups of bundle homeomorphisms

2019 ◽  
pp. 333-339
Author(s):  
Tomasz Rybicki
Keyword(s):  
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.

scholarly journals Uniform perfectness of self-affine sets

2003 ◽  
Vol 131 (10) ◽  
pp. 3053-3057 ◽  
Author(s):  
Feng Xie ◽  
Yongcheng Yin ◽  
Yeshun Sun
Keyword(s):  
Uniform Perfectness

Uniform perfectness of the attractor of bi-Lipschitz IFS

2006 ◽  
Vol 49 (4) ◽  
pp. 433-438 ◽  
Author(s):  
Huojun Ruan ◽  
Yeshun Sun ◽  
Yongcheng Yin
Keyword(s):  
Uniform Perfectness

scholarly journals ON THE UNIFORM PERFECTNESS OF THE BOUNDARY OF MULTIPLY CONNECTED WANDERING DOMAINS

2011 ◽  
Vol 91 (3) ◽  
pp. 289-311 ◽  
Author(s):  
WALTER BERGWEILER ◽  
JIAN-HUA ZHENG
Keyword(s):  
Entire Function ◽  
General Criterion ◽  
Multiply Connected ◽  
Uniformly Perfect ◽  
Wandering Domain ◽  
Uniform Perfectness ◽  
Wandering Domains

AbstractWe investigate when the boundary of a multiply connected wandering domain of an entire function is uniformly perfect. We give a general criterion implying that it is not uniformly perfect. This criterion applies in particular to examples of multiply connected wandering domains given by Baker. We also provide examples of infinitely connected wandering domains whose boundary is uniformly perfect.

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