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Fractals, Wavelets, and their Applications

Contributions from the International Conference and Workshop on Fractals and Wavelets

  • Conference proceedings
  • © 2014

Overview

Editors:
  1. Christoph Bandt

    1. Institut für Mathematik und Informatik, Universität Greifswald, Greifswald, Germany

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  2. Michael Barnsley

    1. Mathematical Sciences Institute, Australian National University, Canberra, Australia

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  3. Robert Devaney

    1. Math Department, Boston University, Boston, USA

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  4. Kenneth J. Falconer

    1. Mathematical Institute, University of St Andrews, St Andrews, Fife, United Kingdom

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  5. V. Kannan

    1. Department of Mathematics and Statistics, University of Hyderabad, Hyderabad, India

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  6. Vinod Kumar P.B.

    1. Department of Basic Sciences & Humanities, Rajagiri School of Engineering & Technology, Kerala, India

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  • Contributions that will inspire and motivate researchers
  • Featuring distinguished mathematicians who are founders of the subjects
  • With new advances into the applications to technology

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 92)

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Table of contents (35 papers)

  1. Front Matter

    Pages i-xii
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  2. Fractal Theory

    1. Front Matter

      Pages 1-1
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    2. Introduction to Fractals

      • Christoph Bandt
      Pages 3-19

    3. Geometry of Self-similar Sets

      • Christoph Bandt
      Pages 21-36

    4. An Introduction to Julia and Fatou Sets

      • Scott Sutherland
      Pages 37-60

    5. Parameter Planes for Complex Analytic Maps

      • Robert L. Devaney
      Pages 61-77

    6. Measure Preserving Fractal Homeomorphisms

      • Michael F. Barnsley, Brendan Harding, Miroslav Rypka
      Pages 79-102

    7. The Dimension Theory of Almost Self-affine Sets and Measures

      • Károly Simon
      Pages 103-127

    8. Countable Alphabet Non-autonomous Self-affine Sets

      • Mariusz Urbański
      Pages 129-145

    9. On Transverse Hyperplanes to Self-similar Jordan Arcs

      • Andrey Tetenov
      Pages 147-156

    10. Fractals in Product Fuzzy Metric Space

      • R. Uthayakumar, A. Gowrisankar
      Pages 157-164

    11. Some Properties on Koch Curve

      • R. Uthayakumar, A. Nalayini Devi
      Pages 165-173

    12. Projections of Mandelbrot Percolation in Higher Dimensions

      • Károly Simon, Lajos Vágó
      Pages 175-190

    13. Some Examples of Finite Type Fractals in Three-Dimensional Space

      • Mai The Duy
      Pages 191-201

    14. Fractals in Partial Metric Spaces

      • S. Minirani, Sunil Mathew
      Pages 203-215

  3. Wavelet Theory

    1. Front Matter

      Pages 217-217
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    2. Frames and Extension Problems I

      • Ole Christensen
      Pages 219-234

    3. Frames and Extension Problems II

      • Ole Christensen, Hong Oh Kim, Rae Young Kim
      Pages 235-243

    4. Local Fractal Functions and Function Spaces

      • Peter R. Massopust
      Pages 245-270

    5. Some Historical Precedents of the Fractal Functions

      • M. A. Navascués, M. V. Sebastián
      Pages 271-282
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Keywords

About this book

Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.

Editors and Affiliations

  • Institut für Mathematik und Informatik, Universität Greifswald, Greifswald, Germany

    Christoph Bandt

  • Mathematical Sciences Institute, Australian National University, Canberra, Australia

    Michael Barnsley

  • Math Department, Boston University, Boston, USA

    Robert Devaney

  • Mathematical Institute, University of St Andrews, St Andrews, Fife, United Kingdom

    Kenneth J. Falconer

  • Department of Mathematics and Statistics, University of Hyderabad, Hyderabad, India

    V. Kannan

  • Department of Basic Sciences & Humanities, Rajagiri School of Engineering & Technology, Kerala, India

    Vinod Kumar P.B.

About the editors

Some key contributors and editors include Robert Devaney, Michael Barnsley, Christoph Bandt, M.Urbanski, Mark Pollicott, Peter Massopust who are the founders of fractals; Scott Sutherland, Jeff Geronimo who are the pioneers in the field of Complex Dynamics; Bin Han, Karoly Simon and Vladimir Protasov who are the experts in the area of Wavelets.

Bibliographic Information

  • Book Title: Fractals, Wavelets, and their Applications

  • Book Subtitle: Contributions from the International Conference and Workshop on Fractals and Wavelets

  • Editors: Christoph Bandt, Michael Barnsley, Robert Devaney, Kenneth J. Falconer, V. Kannan, Vinod Kumar P.B.

  • Series Title: Springer Proceedings in Mathematics & Statistics

  • DOI: https://doi.org/10.1007/978-3-319-08105-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2014

  • Hardcover ISBN: 978-3-319-08104-5Published: 08 October 2014

  • Softcover ISBN: 978-3-319-37563-2Published: 10 September 2016

  • eBook ISBN: 978-3-319-08105-2Published: 27 September 2014

  • Series ISSN: 2194-1009

  • Series E-ISSN: 2194-1017

  • Edition Number: 1

  • Number of Pages: XII, 508

  • Number of Illustrations: 44 b/w illustrations, 81 illustrations in colour

  • Topics: Differential Geometry, Analysis, Algebraic Geometry

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