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Assouad Dimension and Fractal Geometry

£59.99

Part of Cambridge Tracts in Mathematics

  • Date Published: October 2020
  • availability: In stock
  • format: Hardback
  • isbn: 9781108478656

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  • 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.

    • The first thorough treatment of the Assouad dimension in the context of fractal geometry
    • Provides a systematic study using consistent notation of the many variants of the Assouad dimension
    • Discusses several key applications to other fields: number theory, dynamical systems, harmonic analysis, and probability theory
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: October 2020
    • format: Hardback
    • isbn: 9781108478656
    • length: 284 pages
    • dimensions: 235 x 156 x 20 mm
    • weight: 0.53kg
    • availability: In stock
  • Table of Contents

    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.

  • Author

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

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