Real analyticity of Hausdorff dimension for higher-dimensional hyperbolic graph directed Markov systems
type: Item
instance of: scholarly article
title: Real analyticity of Hausdorff dimension for higher-dimensional hyperbolic graph directed Markov systems
zbMATH Open document ID: 1157.37010
author: Mario Roy
author: Mariusz Urbański
published in: Mathematische Zeitschrift
publication date: 2008-08-18T00:00:00Z
review text: 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.
reviewed by: Nicolae-Adrian Secelean
Mathematics Subject Classification ID: 37C45
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37D35
Mathematics Subject Classification ID: 32H50
zbMATH DE Number: 5313077
zbMATH Keywords: graph directed Markov systems
zbMATH Keywords: real analyticity
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: holomorphic and conformal dynamics
MaRDI profile type: Publication
full work available at URL: s00209-007-0267-4
OpenAlex ID: W2016588520
cites work: Analytic multifunctions, holomorphic motions and Hausdorff dimension in iFSs
cites work: Lectures on hyperbolic geometry
cites work: Analytic families of semihyperbolic generalized polynomial-like mappings
cites work: Q4429924
cites work: Gibbs states on the symbolic space over an infinite alphabet
cites work: Dimensions and Measures in Infinite Iterated Function Systems
cites work: Regularity properties of Hausdorff dimension in infinite conformal iterated function systems
cites work: Q4340096
cites work: Thermodynamic formalism for countable Markov shifts
cites work: Lectures on \(n\)-dimensional quasiconformal mappings
DOI: 10.1007/S00209-007-0267-4
Recommended article: The Hausdorff dimension spectrum of conformal graph directed Markov systems and applications to nearest integer continued fractions
Recommended article: The dimension spectrum of conformal graph directed Markov systems
Recommended article: CONTINUITY OF THE HAUSDORFF DIMENSION FOR GRAPH-DIRECTED SYSTEMS
Recommended article: Real analyticity of Hausdorff dimension for expanding rational semigroups
Recommended article: HAUSDORFF DIMENSION OF GENERALIZED MARKOV ATTRACTORS FOR ITERATED FUCTION SYSTEMS
Recommended article: About the $L^2$ analyticity of Markov operators on graphs
Recommended article: Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems
Recommended article: Hausdorff dimension of Markov invariant sets
Recommended article: Hausdorff dimension theorems for self-similar Markov processes
description: scientific article; zbMATH DE number 5313077