Hölder differentiability of self-conformal devil's staircases

DOI10.1017/S0305004113000698zbMath1291.28005arXiv1301.1286WikidataQ56225914 ScholiaQ56225914MaRDI QIDQ5408703

Sascha Troscheit

Publication date: 11 April 2014

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

Full work available at URL: https://arxiv.org/abs/1301.1286

zbMATH Keywords

Hausdorff dimensioniterated function system (devil's staircase)thermodynamic multifractal formalism

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (4)

Differentiability of a two-parameter family of self-affine functions ⋮ Multifractal formalism for generalised local dimension spectra of Gibbs measures on the real line ⋮ Stability and perturbations of countable Markov maps ⋮ Derivatives of slippery Devil's staircases

Cites Work

• The Hausdorff dimension of the nondifferentiability set of a nonsymmetric Cantor function
• Hölder-differentiability of Gibbs distribution functions
• Dimensions of non-differentiability points of Cantor functions
• Non‐differentiability points of Cantor functions
• One-sided multifractal analysis and points of non-differentiability of devils staircases
• Hausdorff dimension of sets of non-differentiability points of Cantor functions
• Thermodynamic Formalism
• The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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