Assouad Dimension and Fractal Geometry - Jonathan M. Fraser

Assouad Dimension and Fractal Geometry

Buch | Hardcover
284 Seiten
2020
Cambridge University Press (Verlag)
978-1-108-47865-6 (ISBN)
83,50 inkl. MwSt
This book is the first thorough treatment of the Assouad dimension in fractal geometry. Aimed at researchers and graduate students, it will have broad appeal among pure mathematicians due to its discussion of the Assouad dimension's many applications to number theory, dynamical systems, harmonic analysis, and probability theory.
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.

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.

Erscheinungsdatum
Reihe/Serie Cambridge Tracts in Mathematics
Zusatzinfo Worked examples or Exercises
Verlagsort Cambridge
Sprache englisch
Maße 156 x 235 mm
Gewicht 530 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Naturwissenschaften Physik / Astronomie Mechanik
ISBN-10 1-108-47865-4 / 1108478654
ISBN-13 978-1-108-47865-6 / 9781108478656
Zustand Neuware
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