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

DOI10.1007/S00209-007-0267-4zbMath1157.37010OpenAlexW2016588520MaRDI QIDQ938270

Mariusz Urbański, Mario Roy

Publication date: 18 August 2008

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-007-0267-4

zbMATH Keywords

Hausdorff dimensionreal analyticitygraph directed Markov systemsholomorphic and conformal dynamics

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Dimension theory of smooth dynamical systems (37C45)

Related Items (6)

Fractal models for normal subgroups of Schottky groups ⋮ Conformal fractals for normal subgroups of free groups ⋮ The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result ⋮ Regularity of Hausdorff measure function for conformal dynamical systems ⋮ Asymptotic solution of Bowen equation for perturbed potentials on shift spaces with countable states ⋮ Lambda-topology versus pointwise topology

Cites Work

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• Lectures on hyperbolic geometry
• Analytic multifunctions, holomorphic motions and Hausdorff dimension in iFSs
• Lectures on \(n\)-dimensional quasiconformal mappings
• Analytic families of semihyperbolic generalized polynomial-like mappings
• Dimensions and Measures in Infinite Iterated Function Systems
• Thermodynamic formalism for countable Markov shifts
• Regularity properties of Hausdorff dimension in infinite conformal iterated function systems
• Gibbs states on the symbolic space over an infinite alphabet

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