Assouad Dimension and Fractal Geometry

Description

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.

Jonathan M. Fraser is a Reader in Mathematics at the University of St Andrews. He works in fractal geometry and related areas.

'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.' Joerg Neunhauserer, European Mathematical Society