Fractal Geometry 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. Multi Fractal Measures
18. Physical Applications
What You Will Learn in Fractal Geometry
"Fractal Geometry: Mathematical Foundations and Applications" by Kenneth Falconer is a definitive introduction to the mathematics of "fractals", exploring their intricate "geometric structures" and irregular patterns. The book emphasizes how seemingly complex shapes can be analyzed using rigorous mathematical tools. Falconer combines theoretical depth with intuitive explanations, making the subject accessible to both students and researchers interested in "measure theory", scaling properties, and the mathematics underlying fractal patterns.
A central focus of the book is the concept of "Hausdorff dimension", which generalizes traditional notions of dimension to quantify the size and complexity of fractals. Falconer also examines self-similar sets, projections, and dimensional calculations, providing a framework for understanding the fine structure of fractal objects. Numerous examples illustrate how fractals appear in nature, mathematics, and applied sciences, linking abstract concepts to real-world phenomena.
Designed for advanced undergraduates, graduate students, and professionals, "Fractal Geometry" balances rigorous proofs with clear explanations and exercises. It equips readers with tools to analyze, construct, and measure fractal objects, emphasizing their applications in mathematics, "geometry", and natural modeling. Falconer’s text remains a cornerstone in fractal studies, providing essential techniques and insights into self-similarity, Hausdorff dimension, and the structure of complex geometric patterns.
Book Details & Specifications
Title:
Fractal Geometry by Kenneth Falconer
Publisher:
John Wiley &Sons
Year:
2003
Pages:
367
Type:
PDF
Language:
English
ISBN-10 #:
111994239X
ISBN-13 #:
978-1119942399
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, renowned for his work in "fractal geometry", "geometric measure theory", and mathematical analysis. He has published extensively on dimensions, self-similar sets, and complex geometric structures, earning recognition as a leading researcher in the field. In "Fractal Geometry", Falconer introduces the theory and applications of fractals, covering "Hausdorff dimension", self-similar sets, and measure-theoretic methods. The book blends rigorous mathematics with clear explanations and examples, making it an essential resource for students and researchers exploring fractals in mathematics, physics, and computer science.
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