Dimensions of harmonic measures on non-autonomous conformal Cantor sets

Abstract We consider non-autonomous conformal iterated function systems (NACIFSs) and their limit sets. Our main focus is on harmonic measure and its dimensions: Hausdorff and packing. We prove that these two dimensions are continuous under perturbations and that they satisfy Bowen’s and Manning’s type formulas. To achieve this, we establish general results about measures, and more broadly about positive functionals, defined on a symbolic space. We also develop tools from thermodynamic formalism in a non-autonomous setting.