Dimension estimates in nonconformal graph directed iterated function systems via asymptotic perturbation

Haruyoshi Tanaka

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arXiv · 2307.10564

Dimension estimates in nonconformal graph directed iterated function systems via asymptotic perturbation

Haruyoshi Tanaka

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Abstract

We consider infinite graph-directed iterated function systems (GIFSs) whose contraction mappings are nonconformal. As our main result, we formulate asymptotic perturbations from conformal GIFSs to nonconformal GIFSs, and give the asymptotic behaviour of the Hausdorff dimension of the limit set of the perturbed system. We also investigate perturbed self-affine sets as special cases.

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Haruyoshi Tanaka. 2023-07-20. Dimension estimates in nonconformal graph directed iterated function systems via asymptotic perturbation. https://arxiv.org/abs/2307.10564

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