Overview
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
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
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)Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Fractal-Based Methods in Analysis
Authors: Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
DOI: https://doi.org/10.1007/978-1-4614-1891-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LCC 2012
Hardcover ISBN: 978-1-4614-1890-0Published: 17 November 2011
Softcover ISBN: 978-1-4899-7374-0Published: 25 January 2014
eBook ISBN: 978-1-4614-1891-7Published: 18 November 2011
Edition Number: 1
Number of Pages: XVI, 408
Topics: Dynamical Systems and Ergodic Theory, Mathematical Methods in Physics, Approximations and Expansions, Mathematical Modeling and Industrial Mathematics, Ordinary Differential Equations