Fractal-Based Methods in Analysis

Fractal-based methods are at the heart of modeling the behavior of phenomena at varying scales. This volume collates techniques for using IFS fractals, including the very latest cutting-edge methods, from more than 20 years of research in this area.

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 inOntario. The major focus of their research is on fractals and the applications of fractals.

Extensive coverage of both the theory and the applications of IFS fractals Unified presentation of almost 20 years of research literature, with new viewpoints and results which stimulate the reader and show the state-of-the-art of research in this area The book illustrates a large number of analytical applications of IFS methods Includes both direct applications of IFS methods as well as new analytical methods inspired by the IFS fractal framework Self-contained and readable mathematical book with background appendices on topological and metric spaces, measure theory, and basic notions from set-valued analysis, which make the book suitable for self-study or for specialized graduate courses Includes supplementary material: sn.pub/extras

Autorentext
Franklin Mendivil is a Professor in the Department of Mathematics and Statistics at Acadia University; Herb Kunze is a Professor in the Department of Mathematics and Statistics at Guelph University; Davide La Torre is an Associate Professor in the Department of Economics, Business and Statistics at University of Milan; Edward R. Vrscay is a Professor at the University of Waterloo.

Klappentext

The idea of modeling the behavior 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 in the Department of Mathematics and Statistics, University of Guelph. Davide La Torre is an Associate Professor in the Department of Economics, Business and Statistics, University of Milan. Franklin Mendivil is a Professor in the Department of Mathematics and Statistics, Acadia University. Edward R. Vrscay is a Professor in the Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo. A major focus of their research is fractals and their applications.

Inhalt
What do we mean by Fractal-Based Analysis".- Basic IFS.- IFS on Spaces of Functions.- IFS, Multifunctions, and Measure-Valued Functions. -IFS on Spaces of Measures.-The Chaos Game.-Inverse Problems and Fractal-Based Methods.-Further Developments and Extensions.- References.- Index.