The Hausdorff dimension of average conformal repellers under random perturbation

TL;DR

This paper demonstrates that the Hausdorff dimension of average conformal repellers remains stable when subjected to random perturbations modeled by bundle random dynamical systems.

Contribution

It introduces a stability result for Hausdorff dimension of average conformal repellers under a new class of random perturbations.

Findings

Hausdorff dimension is stable under random perturbations

Uses bundle random dynamical systems for modeling perturbations

Provides a theoretical proof of stability

Abstract

We prove that the Hausdorff dimension of an average conformal repeller is stable under random perturbations. Our perturbation model uses the notion of a bundle random dynamical system.