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Let = \ₑ\₄ ₄ be a finitely irreducible conformal graph directed Markov system (CGDMS) with symbolic representation EA^ and limit set J. Under a mild condition on the system, we give a multifractal analysis of level sets of Birkhoff averages with respect to Hausdorff dimension for a large family of functions. We then apply these results to a few examples in the case of both E finite and E countably infinite.
Nathan Dalaklis (Sun,) studied this question.