Real analyticity of Hausdorff dimension for higher dimensional hyperbolic graph directed Markov systems

In this paper we prove that the Hausdorff dimension function of the limit sets of strongly regular, hyperbolic, conformal graph directed Markov systems living in higher dimensional Euclidean spaces , , and with an underlying finitely irreducible incidence matrix is real-analytic. Research of M. Roy was supported by NSERC (Natural Sciences and Engineering Research Council of Canada). Research of M. Urbański was supported in part by the NSF Grant DMS 0400481.