Fractals and hyperspaces /
Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorf...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin :
New York : Springer-Verlag,
[1991]
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| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1492. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are "visually fractal", i.e. have infinite detail in a certain sense. These ideas have considerable scope for further development, and a list of problems and lines of research is included. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (168 pages) : illustrations. |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages 160-161) and index. |
| ISBN: | 9783540466109 (electronic bk.) 354046610X (electronic bk.) |
| ISSN: | 0075-8434 ; |