Course No.：S070104ZJ0011
Course Category：Professional Basic Course
Period/Credits：40/2
Prerequisites：Elementary of functions of real variables, Probability theory.
Aims & Requirements：
This course is concerned with the general theory of fractals and their geometry.
Primary Coverage：
Mathematical background: Basic set theory; Functions and limits; Measures and mass; Box-counting dimensions, Hausdorff measures and dimension, Iterated function systems, Graphs of functions, Dynamical systems: Repellers and iterated function systems, The logistic map; Iteration of complex functions: Sketch of general theory of Julia sets.
Textbook：
Fractal Geometry: Mathematical Foundations and applications, K.Falconer, translated by Wenqu Zeng, Posts and Telecom Press, 2007.
References：
[1] Fractal theory and its application, Xia Sun, Ziqin Wu and Yun Huang, China Science and Technology University Press, 2003.
Author：Junxiao Zhao (School of Mathematical Sciences, GUCAS)
Date：June, 2010
