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Iterated function systems with continuous place dependent probabilities. (English) Zbl 1052.28003
Summary: We study the asymptotic behaviour of iterated function systems built of a finite number of contractions and positive, continuous, place dependent probabilities. We prove that these systems have some special property which is called quasistability. We also establish the existence of an invariant distribution for such systems.

MSC:
28A80 Fractals
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37A50 Dynamical systems and their relations with probability theory and stochastic processes
60J05 Discrete-time Markov processes on general state spaces
60J35 Transition functions, generators and resolvents
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