The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of the area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases, they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. “Fractal-based Methods in Analysis” draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints in many of the chapters. For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises. This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. The book is intended for graduate students and researchers in applied mathematics, engineering, and social sciences.
Herb Kunze is a Professor in the Department of Mathematics & Statistics. He obtained his Ph.D. in Applied Mathematics from the University of Waterloo in 1997. His has published over 50 refereed papers on fractal-based methods in analysis, inverse problems, and mathematical imaging. Herb was awarded the UGFA Distinguished Professor Award in 2001, and was the recipient of an OCUFA Teaching Award in 2007.