Fractals, Wavelets, and their Applications

1. Front Matter

   Pages i-xii

   PDF

2. Fractal Theory

   1. Front Matter

      Pages 1-1

      PDF

   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

      PDF

   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

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.

• Fractals
• Iterated Function systems
• Self similarity
• Wavelets

• 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.

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.

Policies and ethics