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Overview"Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an accessible way, complete with many figures. The first part of the book develops certain hyperspace theories 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. 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 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 concepts (defined purely topologically) of self-similarity and fractality: in particular, the author shows that many invariant sets are ""visually fractal"" - 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." Full Product DetailsAuthor: Keith R. WicksPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 1991 ed. Volume: 1492 Dimensions: Width: 15.50cm , Height: 0.90cm , Length: 23.50cm Weight: 0.580kg ISBN: 9783540549659ISBN 10: 354054965 Pages: 172 Publication Date: 27 November 1991 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPreliminaries.- Nonstandard development of the vietoris topology.- Nonstandard development of the Hausdorff metric.- Hutchinson's invariant sets.- Views and fractal notions.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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