Dynamical multifractal zeta-functions, multifractal pressure and fine multifractal spectra

TL;DR

This paper introduces new multifractal pressure and zeta-functions that offer detailed insights into a broad class of multifractal spectra, including those of self-conformal measures and ergodic averages.

Contribution

It presents novel definitions of multifractal pressure and zeta-functions that generalize and refine the understanding of multifractal spectra.

Findings

Provides a framework for analyzing fine multifractal spectra

Applies to self-conformal measures and ergodic Birkhoff averages

Offers precise descriptions of multifractal properties

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 self-conformal measures and the fine multifractal spectra of ergodic Birkhoff averages of continuous functions.