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Uniformly Perfect Analytic and Conformal Attractor Sets
Author(s) -
Stankewitz Rich
Publication year - 2001
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 - 10.1017/s0024609301007950
Subject(s) - attractor , mathematics , conformal map , iterated function system , iterated function , pure mathematics , set (abstract data type) , function (biology) , plane (geometry) , mathematical analysis , geometry , evolutionary biology , computer science , biology , programming language
Conditions are given which imply that analytic iterated function systems (IFSs) in the complex plane C have uniformly perfect attractor sets. In particular, it is shown that the attractor set of a finitely generated conformal IFS is uniformly perfect when it contains two or more points. Also, an example is given of a finitely generated analytic attractor set which is not uniformly perfect.