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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...
| Cote: | Libro Electrónico |
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| Auteur principal: | |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
Cambridge ; New York :
Cambridge University Press,
2011, ©2011.
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| Collection: | Cambridge tracts in mathematics ;
186. |
| Sujets: | |
| Accès en ligne: | Texto completo |
| Résumé: | "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"-- |
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| Description matérielle: | 1 online resource (205 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 196-201) and index. |
| ISBN: | 9780511933530 0511933533 9780511928307 0511928300 9780511930836 0511930836 9780511933912 0511933916 1282931792 9781282931794 |