Dynamical multifractal zeta-functions and fine multifractal spectra of graph-directed self-conformal constructions

TL;DR

This paper introduces multifractal pressure and zeta-functions to analyze detailed multifractal spectra of graph-directed self-conformal measures and ergodic averages, offering a unified approach for complex fractal structures.

Contribution

It develops a general framework of multifractal pressure and zeta-functions to precisely characterize multifractal spectra in graph-directed self-conformal systems.

Findings

Provides a method to compute fine multifractal spectra.

Applies to ergodic Birkhoff averages on self-conformal sets.

Unifies analysis of various multifractal spectra.

Abstract

We introduce multifractal pressure and dynamical multifractal zeta-functions providing precise information of a very general class of multifractal spectra, including, for example, the fine multifractal spectra of graph-directed self-conformal measures and the fine multifractal spectra of ergodic Birkhoff averages of continuous functions on graph-directed self-conformal sets.