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Article Contents

# 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 $(X,\mathbb T_1,\pi_{\lambda}),(Y,\mathbb T_{2},\sigma),h$depending on parameter $\lambda\in\Lambda$ is uniformly contracting (in the generalized sense), then each system of this family admits a compact global attractor $J^{\lambda}$ and the mapping $\lambda \to J^{\lambda}$ is continuous with respect to the Hausdorff metric. As an application we give a generalization of well known Theorem of Bransley concerning the continuous dependence of fractals on parameters.
Mathematics Subject Classification: 37B25, 37B55, 39A11, 39C10, 39C55.

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