Dynamics of Iterative Systems GAČR 201/09/0854

GAČR 201/09/0854
An iterative system consists of a finite number of continuous self-maps of a compact metric space. The maps are iterated in arbitrary order. An iterative system can be conceived as a dynamical system with the role of the time semigroup played by the free semigroup of finite words of an alphabet. The project focuses on clarifying dynamical properties of iterative systems. We shall investigate when these systems are minimal, transitive, chain-transitive and equicontinuous, what are their attractors and their topological entropy. We shall investigate real and complex number systems based on iterative systems consisting of Moebius transformations and will try to find those with fast arithmetical algorithms.