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Assouad Dimension and Fractal Geometry 1st Edition Jonathan M. Fraser

Name: Assouad Dimension and Fractal Geometry 1st Edition Jonathan M. Fraser
SKU: EB-12199818
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Assouad Dimension and Fractal Geometry 1st Edition Jonathan M. Fraser Digital Instant Download

Author(s): Jonathan M. Fraser

ISBN(s): 9781108478656, 9781108778459, 9782020016001, 1108478654, 1108778453, 2020016001, 2020016000

Edition: 1

File Details: PDF, 4.79 MB

Year: 2021

Language: English

SKU: EB-12199818 Category: Mathematics Tag: Jonathan M. Fraser

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ISBN-10 ‏ : ‎ 1108478654
ISBN-13 ‏ : ‎ 978-1108478656
Author: Jonathan M. Fraser

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.

Table of contents:

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

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