The Hausdorff Dimension Of Weierstrass Function

The main work of this article is book review of document[24],which is "the Hausdorff dimension of the graphs of the classical Weierstrass functions". This document solves the Hausdorff dimension of the graphs of the classical Weier-strass functions Wλ1b is equal to 2+logb/logλ, where b≥2, b∈Z, λ∈(1/b,1), which is a conjecture.This article summarizes some theoretical methods used in document [24], including:(1) the related theories of dynamical systems and symbolic space; (2) the proof ideas of this document:the images of such functions Wλ,b can be regarded as the invariant set of the expanding dynamical systems. And thus the Hausdorff dimension of the images of those functions can be studied by the properties of the expanding dynamical systems. As well as the article detailed adds some proof omitted in this document.The first chapter introduces some background knowledge of fractal theory, and related properties of Weierstrass functions; the second chapter describes the main results in document[24], and the related knowledge of dynamical systems; the third chapter summarizes the ideas and processes to solve the argument of the conjecture, and adds proof of which some of the conclusions of the argument is omitted; the fourth chapter gives summary and outlook。...