Fractal-Based Methods in Analysis

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

Table of contents

  1. Front Matter
    Pages i-xv
  2. Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
    Pages 1-19
  3. Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
    Pages 21-85
  4. Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
    Pages 87-123
  5. Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
    Pages 125-147
  6. Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
    Pages 149-212
  7. Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
    Pages 213-241
  8. Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
    Pages 243-314
  9. Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
    Pages 315-355
  10. Back Matter
    Pages 357-408

About this book

Introduction

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.

Keywords

Fractals Image and shape analysis Inverse problems Iterated function systems and self-similar objects Multiscale analysis

Authors and affiliations

  • Herb Kunze
    • 1
  • Davide La Torre
    • 2
  • Franklin Mendivil
    • 3
  • Edward R. Vrscay
    • 4
  1. 1., Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada
  2. 2., Department of Economics, Business and StUniversity of MilanMilanItaly
  3. 3., Department of Mathematics and StatisticsAcadia UniversityWolfvilleCanada
  4. 4., Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-1891-7
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-1890-0
  • Online ISBN 978-1-4614-1891-7
  • About this book