Assouad Dimension and Fractal Geometry

The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.

Table des matières

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.

A propos de l'auteur

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

Résumé

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.

Détails du produit

• Auteurs: Jonathan M Fraser, Jonathan M. Fraser, Jonathan M. (University of St Andrews Fraser, Fraser Jonathan M. Fraser
• Edition: Cambridge University Press ELT
• Langues: Anglais
• Format d'édition: Livre Relié
• Sortie: 30.11.2020
• EAN: 9781108478656
• ISBN: 978-1-108-47865-6
• Pages: 284
• Thèmes: Cambridge Tracts in Mathematics; Cambridge Tracts in Mathematic
• Catégories: Sciences naturelles, médecine, informatique, technique > Mathématiques > Analyse; MATHEMATICS / Geometry / General, MATHEMATICS / Mathematical Analysis, SCIENCE / Mechanics / Dynamics, Calculus & mathematical analysis, Dynamics & statics, Calculus and mathematical analysis, Fractal geometry, SCIENCE / Mechanics / Statics, Dynamics and statics