Hausdorff dimension of sets of non-differentiability points of Cantor functions

DOI10.1017/S0305004100073011zbMath0819.28005OpenAlexW2079517780MaRDI QIDQ4697499

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Publication date: 23 July 1995

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

Full work available at URL: https://doi.org/10.1017/s0305004100073011

zbMATH Keywords

Cantor setHausdorff dimensionCantor functionset of non- differentiability points

Mathematics Subject Classification ID

Singular functions, Cantor functions, functions with other special properties (26A30) Hausdorff and packing measures (28A78) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items (9)

The infinite derivatives of Okamoto's self-affine functions: an application of \(\beta\)-expansions ⋮ Hölder-differentiability of Gibbs distribution functions ⋮ Differentiability of a two-parameter family of self-affine functions ⋮ The Hausdorff dimension of the nondifferentiability set of a nonsymmetric Cantor function ⋮ Cantor type functions in non-integer bases ⋮ Hölder differentiability of self-conformal devil's staircases ⋮ THE DIMENSION OF SETS DETERMINED BY THEIR CODE BEHAVIOR ⋮ The Cantor function ⋮ HOW SMOOTH IS A DEVIL'S STAIRCASE?

Cites Work

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• The Hausdorff Dimension of the Nondifferentiability Set of the Cantor Function is [ ln(2)/ln(3) 2]
• A Characterization of the Nondifferentiability Set of the Cantor Function

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