分形分析
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内容提要：
本书讨论了解形分析，这是一个发展很快的数学分支，主要研究分形的动态特性，如分形的热扩散及分形结构材料的振动。本书从基本的自相似集合的几何学原理开始，逐步对新近的研究成果加以讨论，其中包括拉普拉斯算子的特征值和特征函数的性质、自相似集合热核的渐近特性等。
阅读本书只需具备高等分析学、普通拓扑学和测度论的基础知识。本书特别适合分析和概率论专业的研究生和研究人员阅读，同时本书也非常适合用为与分开有关的研究生课程的初充教材。
作者简介：
Jun Kigami为日本京都大学应用分析与复杂动力系统教授。除本书外，他还与人合著《Mathematics of Fractals》一书。
目录：
Introduction
1 Geometry of Self-Similar Sets 2 Analysis on Limits of Networks 3 Construction of Laplacians on P.C.F.Self-Similar Structures 4 Eigenvalues and Eigenfunctions of Laplacians 5 Heat Kernels Appendix A Additional Facts B Mathematical Background Bibliography Index of Notation Index 前言：
What is "Analysis on Fractals"? Why is it interesting?
To answer those questions, we need to go back to the history of fractals.
Many examples of fractals, like the Sierpinski gasket, the Koch curve and the Cantor set, were already known to mathematicians early in the twentieth century. Those sets were originally pathological (or exceptional) counterexamples. For instance, the Koch curve (see Figure 0.1) is an example of a compact curve with infinite length and the Cantor set is an example of an uncountable perfect set with zero Lebe..
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