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Dimensions, embeddings, and attractors
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Robinson, James C. (2011) Dimensions, embeddings, and attractors. Cambridge tracts in mathematics, Vol.186 . Cambridge ; New York: Cambridge University Press. ISBN 9780521898058
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Official URL: http://webcat.warwick.ac.uk/record=b2341614~S1
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Series Name: | Cambridge tracts in mathematics | ||||
Publisher: | Cambridge University Press | ||||
Place of Publication: | Cambridge ; New York | ||||
ISBN: | 9780521898058 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.186 | ||||
Number of Pages: | 205 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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