Dimensions of harmonic measures on non-autonomous Cantor sets

TL;DR

This paper investigates the harmonic measure on non-autonomous Cantor sets, demonstrating the continuity of Hausdorff and packing dimensions under perturbations and establishing Bowen's and Manning's formulas using thermodynamical formalism.

Contribution

It introduces new results on the dimensions of harmonic measures on non-autonomous Cantor sets and develops thermodynamical tools in a non-autonomous symbolic setting.

Findings

Hausdorff and packing dimensions are continuous under perturbations.

Bowen's and Manning's formulas hold for these measures.

General thermodynamical results for non-autonomous symbolic measures.

Abstract

We consider Non Autonomous Conformal Iterative Function Systems (NACIFS) and their limit set. Our main concern is harmonic measure and its dimensions : Hausdorff and Packing. We prove that this two dimensions are continuous under perturbations and that they verify Bowen's and Manning's type formulas. In order to do so we prove general results about measures, and more generally about positive functionals, defined on a symbolic space, developing tools from thermodynamical formalism in a non-autonomous setting.