Fractured Fractals and Broken Dreams Self-Similar Geometry Through Metric and Measure

Name: Fractured Fractals and Broken Dreams Self-Similar Geometry Through Metric and Measure
Price: 196.94 USD
Availability: InStock
ISBN: 9780198501664

ISBN-10: 0198501668

ISBN-13: 9780198501664

Edition: 1997

Authors: Guy David, Stephen Semmes

List price: $190.00

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Fractal patterns have emerged in many contexts, but what exactly is a pattern? How can one make precise the structures lying within objects and the relationships between them? This book proposes new notions of coherent geometric structure to provide a fresh approach to this familiar field. It develops a new concept of self-similarity called "BPI" or "big pieces of itself," which makes the field much easier for people to enter. This new framework is quite broad, however, and has the potential to lead to significant discoveries. The text covers a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics. Although fractal…

Book details

List price: $190.00
Copyright year: 1997
Publisher: Oxford University Press, Incorporated
Publication date: 2/19/1998
Binding: Hardcover
Pages: 222
Size: 6.14" wide x 9.21" long x 0.67" tall
Weight: 1.012
Language: English




Basic definitions



Examples



Comparison with rectifiability



The Heisenberg group



Background information



Stronger self-similarity for BPI spaces



BPI equivalence



Convergence of metric spaces



Weak tangents



Rest stop



Spaces looking down on other spaces



Regular mappings



Sets made from nested cubes



Big pieces of bilipschitz mappings



Uniformly disconnected spaces



Doubling measures and geometry



Deformations of BPI spaces



Snapshots



Some sets that are far from BPI



A few more questions


References


Index