Assouad dimension of the graph for Takagi function
数学专题报告
报告题目(Title)：Assouad dimension of the graph for Takagi function
报告人(Speaker)：蒋赉 （国科大杭州高等研究院）
地点(Place)：后主楼1220
时间(Time)：2025年3月20日，下午 2:00 - 5:00
邀请人(Inviter)：陈昕昕
报告摘要
This lecture will focus on a series of fractal functions.
For each integer $r \geq 2$, the Takagi function $T_r(x)$ is defined by
$$
T_r(x)=\sum_{n=0}^\infty \frac{\phi(r^n x)}{r^n}, \quad x\in [0,1],
$$
where $\phi(x)={\rm dist}(x,\mathbb{Z})$ is the distance from $x$ to the nearest integer.
We will show that for each integer $r \geq 2$, the Assouad dimension of the graph $\mathcal{G} T_r=\{(x,T_r(x)):x\in[0,1]\}$ for the Takagi function $T_r(x)$ is equal to one, that is,
$$
\dim_A \mathcal{G} T_r=1.
$$
