Attractors of iterated function systems and Markov operators (Q1811866)

The aim of the present paper is to give a review of results concerning ``generalized'' attractors for a large class of iterated function systems \(\{w_i\mid i\in I\}\) acting on a complete separable metric space which allows the consideration of a new class of sets with many interesting properties called semi-attractors or semifractals. Furthermore, the authors present some fixed-point results for Markov operators acting on the space of Borel measures in order to develop some relations between semi-attractors and supports of invariant measures for the aforementioned Markov operators and between multifunctions and transition functions appearing in the theory of Markov operators.