Separation Conditions for Iterated Function Systems with Overlaps

For iterated function systems that have overlaps, various separation conditions have been formulated in the literature to replace the open set condition: the weak separation condition, the weak separation condition*, the finite type condition, and the generalized finite type condition. In this paper we summarize some of the major results concerning these conditions, and clarify their relationships. We also study the question on choosing the invariant open set in the finite type condition.