Fractured Fractals and Broken Dreams: Self-similar Geometry through Metric and Measure

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Guy David (Professor of Mathematics, Professor of Mathematics, University Paris XI and Institut Universitaire de France, France) Stephen Semmes (Professor of Mathematics, Professor of Mathematics, Rice University, Texas, USA)

Fractured Fractals and Broken Dreams

Self-similar Geometry through Metric and Measure

Guy David (Professor of Mathematics, Professor of Mathematics, University Paris XI and Institut Universitaire de France, France), Stephen Semmes (Professor of Mathematics, Professor of Mathematics, Rice University, Texas, USA)

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English

Oxford University Press
01 October 1997

Fractal geometry

Series: Oxford Lecture Series in Mathematics and Its Applications

"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.

One of the main features of the present text is that the basic framework is completely new. This makes it easier for people to get into the field. There are many open problems, with plenty of opportunities that are likely to be close at hand, particularly as concerns the exploration of examples. On the other hand the general framework is quite broad and provides the possibility for future discoveries of some magnitude.

Fractual geometries can arise in many different ways mathematically, but there is not so much general language for making comparisons. This book provides some tools for doing this, and a place where researchers in different areas can find common ground and basic information."

By: Guy David (Professor of Mathematics Professor of Mathematics University Paris XI and Institut Universitaire de France France), Stephen Semmes (Professor of Mathematics, Professor of Mathematics, Rice University, Texas, USA)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Volume: 7
Dimensions: Height: 242mm, Width: 162mm, Spine: 17mm
Weight: 460g
ISBN: 9780198501664
ISBN 10: 0198501668
Series: Oxford Lecture Series in Mathematics and Its Applications
Pages: 224
Publication Date: 01 October 1997
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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

Reviews for Fractured Fractals and Broken Dreams: Self-similar Geometry through Metric and Measure

The book contains a great variety of concepts, examples, results, and open problems...the presentation is both intuitive and precise. Zentralblatt fur Mathematik, 887 Most of the material in this book is completely new and the style, though unusual, is a refreshing change from convetional texts. The authors have taken a natural but not too stront notion relating to sets of fine structure, and follwed through its properties, relationships and applications. They freely admit that their framework is not theonly possible one, but by the end of the book they have more than justified theri claim that their approach is both rich and flexible. The book is recommended not only for those interested in the broad subject of he geometry of fractal sets and measures but also as a fine insight into how two eminent mathematicians explore and develop a new area.