Assouad Dimension and Fractal Geometry

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.

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• A geometria fractal
• Cálculo e análise matemática
• Dinâmica e estática

fractal geometry; dimension theory; Assouad dimension; Asouad spectrum; lower dimension; box dimension; Hausdorff dimension; iterated function system; self-similarity; self-affine set