Diophantine approximation and self-conformal measures

DOI10.1016/j.jnt.2004.07.004zbMath1071.11047OpenAlexW2073582262MaRDI QIDQ1771014

Mariusz Urbański

Publication date: 7 April 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2004.07.004

zbMATH Keywords

Diophantine approximationHausdorff measureGibbs stateAbsolutely friendly measureConformal iterated function systemConformal measureExtremal measureHölder families of functions

Mathematics Subject Classification ID

Metric theory (11J83) Symbolic dynamics (37B10) Diophantine approximation in probabilistic number theory (11K60)

Related Items (11)

Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces ⋮ The set of badly approximable vectors is strongly C¹ incompressible ⋮ Graph directed Markov systems on Hilbert spaces ⋮ Extremality and dynamically defined measures. I: Diophantine properties of quasi-decaying measures ⋮ An extension of quantitative nondivergence and applications to Diophantine exponents ⋮ Schmidt’s game, fractals, and orbits of toral endomorphisms ⋮ METRIC DIOPHANTINE APPROXIMATION FOR SYSTEMS OF LINEAR FORMS VIA DYNAMICS ⋮ Finer Diophantine and regularity properties of 1-dimensional parabolic IFS ⋮ A proof of the matrix version of Baker's conjecture in Diophantine approximation ⋮ Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems ⋮ Badly approximable vectors on fractals

Cites Work

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• Metric Diophantine approximation and `absolutely friendly' measures
• Badly approximable vectors on fractals
• Hausdorff measures versus equilibrium states of conformal infinite iterated function systems
• Flows on homogeneous spaces and Diophantine approximation on manifolds
• On fractal measures and Diophantine approximation
• Thermodynamic formalism and multifractal analysis of conformal infinite iterated function systems
• Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets
• ACHIEVEMENTS AND PROBLEMS IN DIOPHANTINE APPROXIMATION THEORY
• Dimensions and Measures in Infinite Iterated Function Systems

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