TY - JOUR
T1 - Hausdorff Dimension of a Class of Weierstrass Functions
AU - Ruan , Huojun
AU - Zhang , Na
JO - Analysis in Theory and Applications
VL - 4
SP - 482
EP - 496
PY - 2020
DA - 2020/12
SN - 36
DO - http://doi.org/10.4208/ata.OA-SU8
UR - https://global-sci.org/intro/article_detail/ata/18465.html
KW - Hausdorff dimension, Weierstrass function, SRB measure.
AB - <p style="text-align: justify;">It was proved by Shen that the graph of the classical Weierstrass function $\sum_{n=0}^\infty \lambda^n \cos (2\pi b^n x)$ has Hausdorff dimension $2+\log \lambda/\log b$, for every integer $b\geq 2$ and every $\lambda\in (1/b,1)$ [Hausdorff dimension of the graph of the classical Weierstrass functions, Math. Z., 289 (2018), 223–266]. In this paper, we prove that the dimension formula holds for every integer $b\geq 3$ and every $\lambda\in (1/b,1)$ if we replace the function $\cos$ by $\sin$ in the definition of Weierstrass function. A class of more general functions are also discussed.</p>