Iterated function systems with continuous place dependent probabilities. (English) Zbl 1052.28003

Jaroszewska, Joanna

Zesz. Nauk. Uniw. Jagiell. 1258, Univ. Iagell. Acta Math. 40 137-146 (2002).

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

Keywords:

iterated function system; asymptotic stability; IFS; Barnsley operators; attractors; Markov operators