Hostname: page-component-7c8c6479df-ws8qp Total loading time: 0 Render date: 2024-03-28T20:52:59.549Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  17 June 2002

ZHENG JIAN-HUA
Affiliation:
Department of Mathematical Sciences Tsinghua University, Beijing, P.R. China. e-mail: jzheng@math.tsinghua.edu.cn

Abstract

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.

Type
Research Article
Copyright
2002 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)