Shrinking target for $C^1$ weakly conformal IFS with overlaps

TL;DR

This paper investigates the Hausdorff dimension of shrinking targets in weakly conformal iterated function systems with overlaps, extending previous results to systems where conformality and attractor dimensions coincide.

Contribution

It extends existing theories on Hausdorff dimension of shrinking targets to weakly conformal IFSs with overlaps, under the condition that conformality and attractor dimensions are equal.

Findings

Established the Hausdorff dimension for shrinking targets in weakly conformal IFSs with overlaps.

Extended Hill-Velani's results to a broader class of systems.

Generalized previous results for self-similar IFSs to weakly conformal systems.

Abstract

In this article, we study the Hausdor dimension of weakly conformal IFS's shrinking targets with possible overlaps, provided the conformality dimension of the systems and the dimension of the attractor are equal. Those results extends the works of Hill-Velani as well as the results obtained in [6] for self-similar IFS's.