Assouad Dimension and Fractal Geometry

ISBN-13: 9781108478656 / Angielski / Twarda / 2020 / 284 str.

Jonathan M. Fraser

Opis

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.

Recenzje

'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

Spis treści

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.