Continuous Dependence of Attractors on Parameters of Non-Autonomous Dynamical Systems and Infinite Iterated Function Systems

The paper is dedicated to the study of the problem of continuous dependence of compact global attractors on parameters of non-autonomous dynamical systems and infinite iterated function systems (IIFS). We prove that if a family of non-autonomous dynamical systems depending on a parameter is uniformly contracting (in the generalized sense), then each system of this family admits a compact global attractor. As an application we give a generalization of well known Theorem of Bransley concerning the continuous dependence of fractals on parameters.