Hausdorff dimension of local level sets of Takagi's function

摘要

Takagi's function is a continuous nowhere-differentiable function constructed by Takagi in 1903. In this paper, we study the local level sets of Takagi's function. By using the tools of Moran sets and symbolic spaces, we establish the Hausdorff dimension of local level sets for and obtain the range of the Hausdorff dimension. In addition, we derive a lower bound for the Hausdorff dimension of the set of points whose local level set has Hausdorff dimension s.