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arXiv · 1301.4747

Hausdorff dimension of level sets of generalized Takagi functions

Pieter C. Allaart
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Abstract

This paper examines level sets of two families of continuous, nowhere differentiable functions (one a subfamily of the other) defined in terms of the "tent map". The well-known Takagi function is a special case. Sharp upper bounds are given for the Hausdorff dimension of the level sets of functions in these two families. Furthermore, the case where a function f is chosen at random from either family is considered, and results are given for the Hausdorff dimension of the zero set and the set of maximum points of f.

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Pieter C. Allaart. 2013-10-17. Hausdorff dimension of level sets of generalized Takagi functions. https://doi.org/10.1017/s0305004114000309

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