Dimension sets for infinite IFSs: the Texan conjecture

DOI10.1016/J.JNT.2005.04.002zbMath1085.37018OpenAlexW1974527208WikidataQ123144172 ScholiaQ123144172MaRDI QIDQ817740

Sanguo Zhu, Marc Kesseböhmer

Publication date: 20 March 2006

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2005.04.002

zbMATH Keywords

Hausdorff dimensioncontinued fractioniterated function systemsdimension sets

Mathematics Subject Classification ID

Topological dynamics (37B99) Fractals (28A80) Continued fractions; complex-analytic aspects (30B70) Metric theory of continued fractions (11K50) Dimension theory of smooth dynamical systems (37C45)

Related Items (16)

Intermediate dimensions of infinitely generated attractors ⋮ On the dimension spectra of infinite conformal iterated function systems ⋮ Dimension of certain sets of regular and minus continued fractions with positive partial quotients ⋮ The dimension spectrum of conformal graph directed Markov systems ⋮ Parametrizability of infinitely generated attractors ⋮ (Uniform) convergence of twisted ergodic averages ⋮ The Hausdorff dimension spectrum of conformal graph directed Markov systems and applications to nearest integer continued fractions ⋮ A new approach to numerical computation of Hausdorff dimension of iterated function systems: applications to complex continued fractions ⋮ The arithmetic-geometric scaling spectrum for continued fractions ⋮ A remark on densities of hyperbolic dimensions for conformal iterated function systems with applications to conformal dynamics and fractal number theory ⋮ Dimension spectrum of infinite self-affine iterated function systems ⋮ The Hausdorff dimension spectrum of Renyi-like continued fractions ⋮ Diophantine properties of measures invariant with respect to the Gauss map ⋮ A generalization of the Jarník–Besicovitch theorem by continued fractions ⋮ On the dimension spectrum of infinite subsystems of continued fractions ⋮ Limit theorems for counting large continued fraction digits

Cites Work

• Unnamed Item
• A polynomial time algorithm for the Hausdorff dimension of continued fraction Cantor sets
• Hausdorff dimensions of Cantor sets.
• Conformal iterated function systems with applications to the geometry of continued fractions
• Parabolic iterated function systems
• Dimensions and Measures in Infinite Iterated Function Systems
• ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE
• STERN–BROCOT PRESSURE AND MULTIFRACTAL SPECTRA IN ERGODIC THEORY OF NUMBERS

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