Multifractal Analysis of F-exponents for Finitely Irreducible Conformal Graph Directed Markov Systems

Let Φ = \φₑ∈ E 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.