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1	Hausdorff Dimension of Shrinking-Target Sets Under Non-Autonomous Systems Lopez, Marco Antonio 08 1900 (has links) For a dynamical system on a metric space a shrinking-target set consists of those points whose orbit hit a given ball of shrinking radius infinitely often. Historically such sets originate in Diophantine approximation, in which case they describe the set of well-approximable numbers. One aspect of such sets that is often studied is their Hausdorff dimension. We will show that an analogue of Bowen's dimension formula holds for such sets when they are generated by conformal non-autonomous iterated function systems satisfying some natural assumptions. Hausdorff dimension dynamical systems fractal geometry shrinking targets iterated function systems Hausdorff measures. Diophantine approximation. Geometric measure theory.