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＜E-Book＞
Dimensions, Embeddings, and Attractors / James C. Robinson
(Cambridge Tracts in Mathematics ; 186)

Publisher	Cambridge : Cambridge University Press
Year	2010
Size	1 online resource (218 pages) : digital, PDF file(s)
Authors	*Robinson, James C. author
Subjects	LCSH:Dimension theory (Topology) LCSH:Attractors (Mathematics) LCSH:Topological imbeddings
Notes	Title from publisher's bibliographic system (viewed on 14 Nov 2016) 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 HTTP:URL=http://dx.doi.org/10.1017/CBO9780511933912

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