Dimensions, Embeddings, and Attractors
Format: Hardcover
ISBN13: 9780521898058
Hardcover|9780521898058
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Overview
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.
| ISBN-13 | 9780521898058 |
|---|---|
| ISBN-10 | 0521898056 |
| Weight | 0.99 Pounds |
| Dimensions | 6.00 x 0.80 x 9.00 In |
| List Price | $86.99 |
| Edition | 1st Edition |
| Format | Hardcover |
|---|---|
| Language | English |
| Pages | 218 pages |
| Publisher | Cambridge University Press |
| Published On | 2010-12-16 |
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