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arXiv · 2210.05362

Path-dependent shrinking targets in generic affine iterated function systems

Henna Koivusalo·Lingmin Liao·Ian Morris·Michal Rams
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Abstract

We calculate the Hausdorff dimension of shrinking target sets of symbolic balls in generic affine iterated function systems with matrix norms bounded by $\tfrac 12$. Relative to earlier works of e.g. Barany and Troscheit, and Koivusalo and Ramirez, we impose only very mild condition, known as complete reducibility, on the iterated function system. We also generalise these earlier works in that the size of the target in the current work is allowed to depend on the trajectory hitting it. The formula for Hausdorff dimension we obtain is presented as a zero point of certain pressure function.

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Henna Koivusalo, Lingmin Liao, Ian Morris, Michal Rams. 2022-10-11. Path-dependent shrinking targets in generic affine iterated function systems. https://arxiv.org/abs/2210.05362

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