The Geometry of Fractal Sets by Kenneth Falconer
Fractal Geometry - Table of Contents
PART-I FOUNDATIONS
1. Mathematical BackGround
2. Hausdorff Meaure and Dimension
3. Alternative Definitions of Dimension
4. Techniques for Calculating Dimension
5. Local Structure of Fractals
6. Projections of Fractals
7. Products of Fractals
8. Intersections of Fractals
PART-II APPLICATIONS AND EXAMPLES
9. Iterated Function Systems Self Similar and Self Affine Sets
10. Examples from Number Theory
11. Graphs of Functions
12. Examples from Pure Mathematics
13. Dynamical Systems
14. Iteration of Complex Functions - Julia Sets
15. Random Fractals
16. Brownian Motion and Brownian Surfaces
17. MultiFractal Measures
18. Physical Applications
What You Will Learn in Fractal Geometry
"Fractal Geometry: Mathematical Foundations and Applications" by Kenneth Falconer is a classic text that introduces the mathematics of "fractals" and their complex "geometric properties". The book explores how irregular, fragmented sets can be analyzed using rigorous mathematical tools. Falconer provides a clear introduction to the theory of self-similar and fractal sets, emphasizing both intuition and formal proofs. This text serves as a foundational resource for anyone studying the structure and complexity of fractal objects.
A central theme of the book is the "Hausdorff dimension", which allows mathematicians to measure the size of fractal sets in a way that extends traditional dimensions. Falconer also discusses "self-similarity", scaling behavior, and measure-theoretic approaches to study the intricate structure of fractals. Numerous examples illustrate how these abstract concepts apply to real-world phenomena, including natural shapes, irregular mathematical sets, and other applications in "geometry" and analysis.
Designed for graduate students, researchers, and enthusiasts, "The Geometry of Fractal Sets" balances formal mathematical rigor with illustrative examples. Exercises and explanations encourage readers to apply methods and develop a deeper understanding of fractal structures. The book remains a key reference for studying "measure theory", self-similarity, Hausdorff dimension, fractals, and the "geometric intricacy" of complex sets in mathematics and science.
Book Details & Specifications
Title:
The Geometry of Fractal Sets by Kenneth Falconer
Publisher:
John Wiley &Sons
Year:
1990
Pages:
155
Type:
PDF
Language:
English
ISBN-10 #:
0521337054
ISBN-13 #:
978-0521337052
License:
University Educational Resource
Amazon:
Amazon
About the Author: Kenneth Falconer
The author Kenneth Falconer
is a British "mathematician" and professor at the University of St Andrews, known for his research in "fractal geometry", "geometric measure theory", and mathematical analysis. He has published widely on dimensions, self-similar sets, and the structure of complex geometric objects, earning recognition as a leading figure in fractal mathematics. In "The Geometry of Fractal Sets", Falconer explores the properties of irregular and self-similar sets, emphasizing "Hausdorff dimension" and measure-theoretic methods. The book offers a rigorous yet accessible approach, making it an essential reference for students and researchers studying the mathematical foundations and applications of fractals.
Read or Downloadable Fractal Geometry
Free Geometry Books PDF | Curated Academic Library Index