Weak tangents and level sets of Takagi functions

2016/11/13 by Han Yu, Yu, Han
Mathematics · #26A27 #28A80 #37C45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26A27 #msc:28A80 #msc:37C45

paper · pdf · doi:10.48550/arxiv.1611.04172

14 pages

arxiv created 2018/05/01 · arxiv updated 2018/05/03

Abstract

In this paper we study some properties of Takagi functions and their level sets. We show that for Takagi functions T_a,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 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.

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