Premium
Normality and attracting fixed points
Author(s) -
Chang Jianming,
Fang Mingliang,
Zalcman Lawrence
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn056
Subject(s) - meromorphic function , iterated function , mathematics , fixed point , normality , domain (mathematical analysis) , integer (computer science) , unit (ring theory) , complex plane , plane (geometry) , construct (python library) , unit circle , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , geometry , computer science , statistics , mathematics education , programming language
Let k ⩾ 2 be a fixed integer. We construct a non‐normal family of meromorphic functions in the unit disc with k th iterates that have no non‐attracting fixed points in the unit disc. We also prove that a family of meromorphic functions in a plane domain is normal if all fixed points in the domain of the k ‐iterates of all functions in the family are uniformly attracting.