Dimensions, Embeddings, and Attractors
Author | : James C. Robinson |
Publisher | : Cambridge University Press |
Total Pages | : 219 |
Release | : 2010-12-16 |
ISBN-10 | : 9781139495189 |
ISBN-13 | : 1139495186 |
Rating | : 4/5 (186 Downloads) |
Download or read book Dimensions, Embeddings, and Attractors written by James C. Robinson and published by Cambridge University Press. This book was released on 2010-12-16 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.