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

ISBN-13: 9780198501664 / Angielski / Twarda / 1998 / 224 str.

Guy R. David; Stephen W. Semmes; Guy Rene Pierre Pierre

Opis

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 geometries arise in many different ways mathematically, comparing them has been difficult. This new approach combines accessibility with powerful tools for comparing fractal geometries, making it an ideal source for researchers in different areas to find both common ground and basic information.

Recenzje

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.