Assouad Dimension and Fractal Geometry

The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.

Jonathan M. Fraser (Author)

9781108478656, Cambridge University Press

Hardback, published 29 October 2020

284 pages
23.5 x 15.6 x 2 cm, 0.53 kg

'The book is very well written and illustrated. The reader gets to know an almost complete spectrum of resent results and historical developments concerning Assouad dimension.' Jörg Neunhäuserer, European Mathematical Society

The Assouad dimension is a notion of dimension in fractal geometry that has been the subject of much interest in recent years. This book, written by a world expert on the topic, is the first thorough account of the Assouad dimension and its many variants and applications in fractal geometry and beyond. It places the theory of the Assouad dimension in context among up-to-date treatments of many key advances in fractal geometry, while also emphasising its diverse connections with areas of mathematics including number theory, dynamical systems, harmonic analysis, and probability theory. A final chapter detailing open problems and future directions for research brings readers to the cutting edge of this exciting field. This book will be an indispensable part of the modern fractal geometer's library and a valuable resource for pure mathematicians interested in the beauty and many applications of the Assouad dimension.

Part I. Theory: 1. Fractal geometry and dimension theory
2. The Assouad dimension
3. Some variations on the Assouad dimension
4. Dimensions of measures
5. Weak tangents and microsets
Part II. Examples: 6. Iterated function systems
7. Self-similar sets
8. Self-affine sets
9. Further examples: attractors and limit sets
10. Geometric constructions
11. Two famous problems in geometric measure theory
12. Conformal dimension
Part III. Applications: 13. Applications in embedding theory
14. Applications in number theory
15. Applications in probability theory
16. Applications in functional analysis
17. Future directions
References
List of notation
Index.

Subject Areas: Dynamics & statics [PHDT], Fractal geometry [PBMX], Calculus & mathematical analysis [PBK]