Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 1
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    WANG, XIAOLING and ZHOU, WANG 2007. Uniformly bounded components of normality. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 143, Issue. 01, p. 85.


    ×
  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 132, Issue 3
  • May 2002, pp. 531-544

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

  • ZHENG JIAN-HUA (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004101005813
  • Published online: 01 June 2002
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.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×