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