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 ...
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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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Add this copy of Dimensions, Embeddings, and Attractors to cart. $78.31, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2010 by Cambridge University Press.
Add this copy of Dimensions, Embeddings, and Attractors to cart. $95.04, new condition, Sold by Booksplease rated 3.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2010 by Cambridge University Press.
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New. Contains: Line drawings, Halftones, Unspecified. Cambridge Tracts in Mathematics . 10 b/w illus. 60 exercises. Intended for professional and scholarly audience.
Add this copy of Dimensions, Embeddings, and Attractors to cart. $88.39, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2010 by Cambridge University Press.
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New. Print on demand Contains: Line drawings, Halftones, Unspecified. Cambridge Tracts in Mathematics . 10 b/w illus. 60 exercises. Intended for professional and scholarly audience.
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