Hausdorff Dimension of Shrinking-Target Sets Under Non-Autonomous Systems

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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.

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Lopez, Marco Antonio August 2018.

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  • Lopez, Marco Antonio

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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.

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  • August 2018

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  • Sept. 26, 2018, 6:16 p.m.

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Lopez, Marco Antonio. Hausdorff Dimension of Shrinking-Target Sets Under Non-Autonomous Systems, dissertation, August 2018; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc1248505/: accessed October 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .