Uniformly perfect analytic and conformal non-autonomous attractor sets

Abstract

Conditions are given which imply that certain non-autonomous analytic iterated function systems (NIFS's) in the complex plane C have uniformly perfect attractor sets. Examples are given to illustrate the main theorem, as well as to indicate how it generalizes other results. Examples are also given to illustrate how natural generalizations of corresponding results for autonomous IFS's do not hold in general in this more flexible setting.