Robinson, James C. (James Cooper), 1969- (2011) Dimensions, embeddings, and attractors. Cambridge tracts in mathematics, Vol.186 . Cambridge University Press, Cambridge ; New York. ISBN 9780521898058

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Abstract

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.

Item Type:	Book
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Series Name:	Cambridge tracts in mathematics
Publisher:	Cambridge University Press
Place of Publication:	Cambridge ; New York
ISBN:	9780521898058
Date:	2011
Volume:	Vol.186
Number of Pages:	205
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/43940

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