Dimensions, Embeddings, and Attractors - Cambridge Tracts in Mathematics
Dimensions, Embeddings, and Attractors - Cambridge Tracts in Mathematics
hardback
Published:
16 December, 2010
hardback
Published:
16 December, 2010
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Description
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.
More Details
| Type | Book |
|---|---|
| ISBN13 | 9780521898058 |
| ISBN10 | 0521898056 |
| Number Of Pages | 218 |
| Item Weight | 450 g |
| Product Dimensions | 160 x 235 x 20 mm |
| Publisher / Reseller | Cambridge University Press |
| Format | hardback |
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Author's Bio
James C. Robinson is Professor of Mathematics at Warwick University.