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Description - Dimensions, Embeddings, and Attractors by James C. Robinson

This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering dimension (from classical 'dimension theory'), Hausdorff dimension (from geometric measure theory), upper box-counting dimension (from dynamical systems), and Assouad dimension (from the theory of metric spaces). These abstract embedding results are applied in the second part of the book to the finite-dimensional global attractors that arise in certain infinite-dimensional dynamical systems, deducing practical consequences from the existence of such attractors: a version of the Takens time-delay embedding theorem valid in spatially extended systems, and a result on parametrisation by point values. This book will appeal to all researchers with an interest in dimension theory, particularly those working in dynamical systems.

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Book Details

ISBN: 9780521898058
ISBN-10: 0521898056
Format: Hardback
(228mm x 152mm x 20mm)
Pages: 218
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 16-Dec-2010
Country of Publication: United Kingdom

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Author Biography - James C. Robinson

James C. Robinson is Professor of Mathematics at Warwick University.

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