Saved in:
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2011
|
| Series: | Cambridge tracts in mathematics
186 |
| Links: | https://doi.org/10.1017/CBO9780511933912 |
| Summary: | 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. |
| Physical Description: | 1 Online-Ressource (xii, 205 Seiten) |
| ISBN: | 9780511933912 |
Staff View
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| spelling | Robinson, James C. 1969- Dimensions, embeddings, and attractors James C. Robinson Dimensions, Embeddings, & Attractors Cambridge Cambridge University Press 2011 1 Online-Ressource (xii, 205 Seiten) txt c cr Cambridge tracts in mathematics 186 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. Erscheint auch als Druck-Ausgabe 9780521898058 |
| spellingShingle | Robinson, James C. 1969- Dimensions, embeddings, and attractors |
| title | Dimensions, embeddings, and attractors |
| title_alt | Dimensions, Embeddings, & Attractors |
| title_auth | Dimensions, embeddings, and attractors |
| title_exact_search | Dimensions, embeddings, and attractors |
| title_full | Dimensions, embeddings, and attractors James C. Robinson |
| title_fullStr | Dimensions, embeddings, and attractors James C. Robinson |
| title_full_unstemmed | Dimensions, embeddings, and attractors James C. Robinson |
| title_short | Dimensions, embeddings, and attractors |
| title_sort | dimensions embeddings and attractors |
| work_keys_str_mv | AT robinsonjamesc dimensionsembeddingsandattractors AT robinsonjamesc dimensionsembeddingsattractors |