Abstract
AbstractIn this paper, we study some properties of Takagi functions and their level sets. We show that for Takagi functions $$T_{a,b}$$Ta,b with parameters a, b such that ab is a root of a Littlewood polynomial, there exist large level sets. As a consequence, we show that for some parameters a, b, the Assouad dimension of graphs of $$T_{a,b}$$Ta,b is strictly larger than their upper box dimension. In particular, we can find weak tangents of those graphs with large Hausdorff dimension, larger than the upper box dimension of the graphs.
Funder
H2020 European Research Council
Publisher
Springer Science and Business Media LLC
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