Escape rates for Gibbs measures

TL;DR

This paper investigates how Gibbs measures escape through small holes in conformal repellers and explores implications for the Hausdorff dimension of survivor sets.

Contribution

It provides new insights into the asymptotic escape rates of Gibbs measures and their effect on the Hausdorff dimension of survivor sets.

Findings

Derived asymptotic formulas for escape rates.

Established connections between escape rates and Hausdorff dimension.

Applied results to conformal repellers and survivor sets.

Abstract

We study the asymptotic behaviour of the escape rate of a Gibbs measure supported on a conformal repeller through a small hole. There are additional applications to the convergence of Hausdorff dimension of the survivor set.