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

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