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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2011, ©2011.
|
| Colección: | Cambridge tracts in mathematics ;
186. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Robinson, James C. |q (James Cooper), |d 1969- | |
| 245 | 1 | 0 | |a Dimensions, embeddings, and attractors / |c James C. Robinson. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2011, ©2011. | ||
| 300 | |a 1 online resource (205 pages) : |b illustrations | ||
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| 490 | 1 | |a Cambridge tracts in mathematics ; |v 186 | |
| 520 | |a "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"-- |c Provided by publisher | ||
| 504 | |a Includes bibliographical references (pages 196-201) and index. | ||
| 505 | 0 | |a 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. | |
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Dimension theory (Topology) | |
| 650 | 0 | |a Attractors (Mathematics) | |
| 650 | 0 | |a Topological imbeddings. | |
| 650 | 6 | |a Théorie de la dimension (Topologie) | |
| 650 | 6 | |a Attracteurs (Mathématiques) | |
| 650 | 6 | |a Plongements topologiques. | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations. |2 bisacsh | |
| 650 | 7 | |a Attractors (Mathematics) |2 fast | |
| 650 | 7 | |a Dimension theory (Topology) |2 fast | |
| 650 | 7 | |a Topological imbeddings |2 fast | |
| 650 | 7 | |a Topologische Einbettung |2 gnd | |
| 650 | 7 | |a Dimension n |2 gnd | |
| 650 | 7 | |a Seltsamer Attraktor |2 gnd | |
| 776 | 0 | 8 | |i Print version: |a Robinson, James C. (James Cooper), 1969- |t Dimensions, Embeddings, and Attractors. |d Cambridge ; New York : Cambridge University Press, 2011, ©2011 |z 9780521898058 |w (DLC) 2010042726 |w (OCoLC)676062809 |
| 830 | 0 | |a Cambridge tracts in mathematics ; |v 186. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=344640 |z Texto completo |
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