Hausdorff dimension of the limit set of conformal iterated function systems with overlaps

DOI10.1090/S0002-9939-2011-10704-4zbMath1234.37020OpenAlexW1980311114MaRDI QIDQ3020363

Mariusz Urbański, Eugen Mihailescu

Publication date: 4 August 2011

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-10704-4

zbMATH Keywords

Hausdorff dimensionequilibrium statesoverlapsconformal iterated function systems

Mathematics Subject Classification ID

Fractals (28A80) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dimension theory of smooth dynamical systems (37C45)

Related Items (6)

Overlap functions for measures in conformal iterated function systems ⋮ Ruelle operator for infinite conformal iterated function systems ⋮ Asymptotic order of the quantization errors for a class of self-affine measures ⋮ Quantization coefficients in infinite systems ⋮ Bivariate shape preserving interpolation: a fractal-classical hybrid approach ⋮ Quantization dimension estimate of probability measures on hyperbolic recurrent sets

Cites Work

• Unstable directions and fractal dimension for skew products with overlaps in fibers
• Non-linear iterated function systems with overlaps
• Graph directed Markov systems on Hilbert spaces
• Inverse Pressure Estimates and the Independence of Stable Dimension for Non-Invertible Maps
• Hausdorff dimension for horseshoes in $\mathbb{R}^3$
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