Hausdorff Dimension of a Class ofWeierstrass Functions  

作　　者：Huojun Ruan Na Zhang 

机构地区：[1]School of Mathematical Sciences,Zhejiang University,Hangzhou,Zhejiang 310027,China

出　　处：《Analysis in Theory and Applications》2020年第4期482-496,共15页分析理论与应用（英文刊）

摘　　要：It was proved by Shen that the graph of the classical Weierstrass function∑∞n=0λn cos(2πbnx)has Hausdorff dimension 2+logλ/log b,for every integer b≥2 and everyλ∈(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≥3 and everyλ∈2(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.

关 键 词：Hausdorff dimension Weierstrass function SRB measure. 

分 类 号：O174[理学—数学]