| Description |
1 online resource (205 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Cambridge tracts in mathematics ; 186
|
|
Cambridge tracts in mathematics ; 186.
|
| 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"-- Provided by publisher. |
| Bibliography |
Includes bibliographical references (pages 196-201) and index. |
| Contents |
Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; Introduction; PART I: Finite-dimensional sets; 1 Lebesgue covering dimension; 2 Hausdorff measure and Hausdorff dimension; 3 Box-counting dimension; 4 An embedding theorem for subsets of RN in terms of the upper box-counting dimension; 5 Prevalence, probe spaces, and a crucial inequality; 6 Embedding sets with dH(X -- X) finite; 7 Thickness exponents; 8 Embedding sets of finite box-counting dimension; 9 Assouad dimension; PART II: Finite-dimensional attractors; 10 Partial differential equations and nonlinear semigroups. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Dimension theory (Topology)
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Dimension theory (Topology) |
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Attractors (Mathematics)
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Attractors (Mathematics) |
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Topological imbeddings.
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Topological imbeddings. |
| Genre/Form |
Electronic books.
|
| Other Form: |
Print version: Robinson, James C. (James Cooper), 1969- Dimensions, Embeddings, and Attractors. Cambridge ; New York : Cambridge University Press, 2011, ©2011 9780521898058 (DLC) 2010042726 (OCoLC)676062809 |
| ISBN |
9780511933530 (electronic book) |
|
0511933533 (electronic book) |
|
9780511928307 (electronic book) |
|
0511928300 (electronic book) |
|
9780511930836 (electronic book) |
|
0511930836 (electronic book) |
|
9780511933912 (electronic book) |
|
0511933916 (electronic book) |
|
1282931792 |
|
9781282931794 |
|
9780521898058 |
|
0521898056 |
| Standard No. |
9786612931796 |
|
