Fractal Geometry: Mathematical Foundations and Applications by Kenneth Falconer
Fractal Geometry - Table of Contents
PART-I FOUNDATIONS
- 1. Mathematical Background
- 2. Hausdorff Measure 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 reference designed for advanced undergraduate and graduate mathematics scholars. Functioning as an indispensable manual for measure theory and dimension theory, this third edition serves as a core resource for fractal geometry mathematical foundations problem solving practice.
The book systematically investigates Hausdorff dimension, box-counting dimensions, iterated function systems, self-similar sets, multi-fractal analysis, and dynamical systems. By combining rigorous measure-theoretic proofs with physical and biological modeling, Falconer enables researchers to carry out essential fractal geometry dimension calculation derivations with absolute mathematical rigor.
Widely recognized for its clean progression and comprehensive topic coverage, this treatise remains a standard text across geometry and mathematical physics. Falconer’s lucid structure arms readers with analytical tools required for mastering modern fractal geometry principles in contemporary research.
Book Details & Specifications
Title:
Fractal Geometry: Mathematical Foundations and Applications 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 Professor of Mathematics at the University of St Andrews, renowned worldwide for his fundamental contributions to fractal geometry and geometric measure theory.
Throughout his distinguished career, Professor Falconer has authored influential textbooks, delivering comprehensive reference material and advanced fractal geometry study guides for students and researchers across the globe.
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