Fractal measures for parabolic IFS

DOI10.1006/AIMA.2001.2049zbMath1013.28007OpenAlexW2000583998MaRDI QIDQ696842

R. Daniel Mauldin, Mariusz Urbański

Publication date: 12 September 2002

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/1abc48e8fdc567ac8898a960d28f719676bece31

zbMATH Keywords

Hausdorff dimensioniterated function systemHausdorff measureparabolic iterated function systemsbox-counting dimensionIFSpacking measureparabolic conformal diffeomorphism

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78) Dynamical systems over complex numbers (37F99)

Related Items (5)

Parametrizability of infinitely generated attractors ⋮ Real analyticity of topological pressure for parabolically semihyperbolic generalized polynomial-like maps ⋮ Finer Diophantine and regularity properties of 1-dimensional parabolic IFS ⋮ Smale endomorphisms over graph-directed Markov systems ⋮ Spectral Properties of Laplacians on Snowflake Domains and Filled Julia Sets

Cites Work

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• Lectures on hyperbolic geometry
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• Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets
• Rigidity of multi-dimensional conformal iterated function systems
• Geometric measures for parabolic rational maps
• Conformal iterated function systems with applications to the geometry of continued fractions
• Rational functions with no recurrent critical points
• Parabolic iterated function systems
• Dimensions and Measures in Infinite Iterated Function Systems

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