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About Dimensions, embeddings, and attractors
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.
Detailed Information
| Author: | Robinson J.C. |
|---|---|
| Publication Year: | 2011 |
| ISBN: | 9780521898058 |
| Pages: | 219 |
| Language: | English |
| File Size: | 1.116 |
| Format: | |
| Price: | FREE |
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