Mathematical Foundations and Methods in Fractal Applications

Author: Xie Heping, Xue Xiupan (editors)
Publisher:
Publish Date: 2005-03-10
Features: Fractal theory is a new discipline for studying nonlinear problems. Since Mandelbrot first proposed fractals in the 1970s, this discipline has rapidly developed both in its mathematical foundations and in its applications to other fields. This book provides a detailed introduction to the mathematical foundations and methods of fractal applications. The main contents include: sets and metric spaces, fractal spaces, self-similar fractals and self-affine fractals, Lebesgue measure and Hausdorff measure, fractal dimensions and multifractal dimensions, the structure of fractals and iterative function systems, dynamical systems on fractals and Julia sets and the Mandelbrot set, stochastic fractals and stochastic processes on fractal sets, fractal interpolation methods and fractal approximation methods, the Dirichlet problem on fractal boundaries, and finally, mechanics problems on fractal spaces. Each chapter includes a certain number of examples and exercises. The book pays attention to the systematicity of the mathematical foundations of fractal theory and the practicality of the methods, making it suitable for scientists and engineers engaged in fractal research, as well as serving as a teaching reference for higher education institutions.