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.
| ISBN: | 9780521898058 |
| Publication date: | 16th December 2010 |
| Author: | James C University of Warwick Robinson |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 218 pages |
| Series: | Cambridge Tracts in Mathematics |
| Genres: |
Differential calculus and equations Functional analysis and transforms |
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.
Dimensions, Embeddings, and Attractors features in the following genres: Differential calculus and equations, Functional analysis and transforms
Dimensions, Embeddings, and Attractors is available in Hardback
Dimensions, Embeddings, and Attractors was written by James C University of Warwick Robinson and published by Cambridge University Press
Dimensions, Embeddings, and Attractors has 218 pages
Yes it is part of Cambridge Tracts in Mathematics series
£60.30