Graph directed Markov systems on Hilbert spaces

DOI10.1017/S0305004109002448zbMath1177.37054MaRDI QIDQ3183168

Mariusz Urbański, Tomasz Szarek, R. Daniel Mauldin

Publication date: 19 October 2009

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

metric spacescompactnessHausdorff dimensionlimit setstopological pressurePolish spacesgraph directed Markov systemsBowen's formulaconformal measures4r-covering theoremco-Frostman-type theoremscontracting iterated function systemsgeometrically perfect measures

Mathematics Subject Classification ID

Iteration theory, iterative and composite equations (39B12) Hausdorff and packing measures (28A78) Random dynamical systems (37H99) Dimension theory of smooth dynamical systems (37C45) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15) Geometric limits in holomorphic dynamics (37F40)

Related Items (17)

Dimension of invariant measures for continuous random dynamical systems ⋮ Extremality and dynamically defined measures. I: Diophantine properties of quasi-decaying measures ⋮ A Hausdorff measure version of the Jarník–Schmidt theorem in Diophantine approximation ⋮ Decaying and non-decaying badly approximable numbers ⋮ The Hausdorff dimension of the harmonic measure for relatively hyperbolic groups ⋮ On the connectedness of attractors of orbital contractive IFSs ⋮ A variational principle in the parametric geometry of numbers ⋮ Parametrizability of infinitely generated attractors ⋮ CONTINUITY OF THE HAUSDORFF DIMENSION FOR GRAPH-DIRECTED SYSTEMS ⋮ On interpreting Patterson–Sullivan measures of geometrically finite groups as Hausdorff and packing measures ⋮ Infinite graph-directed systems and Hausdorff dimension ⋮ Conformal Graph Directed Markov Systems on Carnot Groups ⋮ Dimension rigidity in conformal structures ⋮ Dimension of harmonic measures in hyperbolic spaces ⋮ Hausdorff dimension of the limit set of conformal iterated function systems with overlaps ⋮ A remark on densities of hyperbolic dimensions for conformal iterated function systems with applications to conformal dynamics and fractal number theory ⋮ Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems

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