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 this 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 and results 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. This book is
intended for graduate students and researchers in applied mathematics,
engineering and social sciences.
Herb Kunze is a professor of mathematics at the University of Guelph in
Ontario. Davide La Torre is an associate professor of mathematics in the
Department of Economics, Management and Quantitative Methods of the
University of Milan. Franklin Mendivil is a professor of mathematics at
Acadia University in Nova Scotia. Edward Vrscay is a professor in the
department of Applied Mathematics at the University of Waterloo in
Ontario. The major focus of their research is on fractals and the
applications of fractals.
