Guy David, Stephen Semmes

Fractured Fractals and Broken Dreams

Self-Similar Geometry Through Metric and Measure

• Gebundenes Buch

Produktbeschreibung

Fractal geometrics can arise in many different ways mathematically. This book proposes notions of coherent geometric structure, asking what exactly is a fractal "pattern"? A wide range of problems are dealt with, and examples given, which connect to other diverse areas of mathmatics.

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This book proposes new notions of coherent geometric structure. Fractal patterns have emerged in many contexts, but what exactly is a `pattern' and what is not? How can one make precise the structures lying within objects and the relationships between them? The foundations laid herein provide a fresh approach to a familiar field. From this emerges a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics.

Produktdetails

• Verlag: Oxford University Press, USA
• Seitenzahl: 224
• Erscheinungstermin: 19. Februar 1998
• Englisch
• Abmessung: 234mm x 156mm x 14mm
• Gewicht: 490g
• ISBN-13: 9780198501664
• ISBN-10: 0198501668
• Artikelnr.: 33372897

Inhaltsangabe

1: Basic definitions
2: Examples
3: Comparison
4: The Heisenberg group
5: Background information
6: Stronger self-similarity for BPI spaces
7: BPI equivalence
8: Convergence of metric spaces
9: Weak tangents
10: Rest stop
11: Spaces looking down on other spaces
12: Regular mappings
13: Sets made from nested cubes
14: Big pieces of bilipschitz mappings
15: Uniformly disconnected spaces
16: Doubling measures and geometry
17: Deformations of BPI spaces
18: Snapshots
19: Some sets that are far from BPI
20: A few more questions
References
Index