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

TL;DR

This paper studies how the Hausdorff dimension of limit sets in nonconformal graph-directed iterated function systems changes under small perturbations, providing asymptotic formulas and insights.

Contribution

It introduces a method to analyze the asymptotic behavior of Hausdorff dimension in nonconformal GIFSs via perturbation from conformal systems.

Findings

Asymptotic formulas for Hausdorff dimension under perturbations

Extension of results to perturbed self-affine sets

Insights into dimension stability in nonconformal systems

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.