Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay

Fractal-Based Methods in Analysis (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 408
• Erscheinungstermin: 18. November 2011
• Englisch
• ISBN-13: 9781461418917
• Artikelnr.: 37357462

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

From the reviews:
"This book intends to introduce the prospective reader to a variety of fractal-based methods in analysis. ... The book is accessible to graduate students with a solid understanding of real analysis, functional analysis, and probability theory, but it seems to be primarily aimed at mathematicians who like to employ fractal-based methodologies in their research." (Peter R. Massopust, Mathematical Reviews, September, 2013)