Random dynamical systems arising from iterated function systems with place-dependent probabilities
The authors assume that a given iterated function system (IFS) admits an invariant and attractive measure. Under this assumption, the authors then construct a probability space \((S,V,P)\) and an ergodic mapping \(f\) related to this IFS. The authors prove that the IFS considered has the structure of a random dynamical system with time \(T\) as the set of natural numbers. If, in addition, it is an IFS of homeomorphisms, then the time can be extended to all integers. The random dynamical systems have been studied here from the point of view of \textit{L. Arnold} [Random dynamical systems, Springer (1998; Zbl 0906.34001)].
scientific article; zbMATH DE number 1556862
scientific article