Real analyticity of Hausdorff dimension for higher-dimensional hyperbolic graph directed Markov systems
The authors consider the problem of regularity of the Hausdorff dimension function of the limit sets of strongly regular, hyperbolic, conformal graph directed Markov systems systems living in higher dimensional Euclidean space \(\mathbb{R}^d\), \(d\geq 3\), and whose underlying finitely irreducible incidence matrix. It is proved that the Hausdorff dimension function of the limits sets in that case is real-analytic. The main result is contained in Theorem 7.2. The article is very well written and the subject is very actual.
scientific article; zbMATH DE number 5313077
scientific article