| The aim of this work is the study of infinite conformal iterated function systems. More specifically, we investigate some properties of a limit set J associated to such system, its measure and Hausdorff dimension. We provide necessary and sufficient conditions for such systems to be bi-Lipschitz equivalent. We use the concept of scaling functions to obtain some result about 1-dimensional systems.;We discuss particular examples of conformal repellers, obtained as limit sets of iterated function systems derived from complex continued fraction expansions with restricted entries. Each system is obtained from an infinite number of contactions. We show that under certain conditions the repellers possess zero Hausdorff measure and positive finite packing measure.;In this thesis we also use the concept of an iterated function system to construct a natural wide class of positively recurrent functions with strong ergodic properties. |
