Dimensions, Embeddings, and Attractors

Dimensions, Embeddings, and Attractors
Author :
Publisher : Cambridge University Press
Total Pages : 219
Release :
ISBN-10 : 9781139495189
ISBN-13 : 1139495186
Rating : 4/5 (186 Downloads)

Book Synopsis Dimensions, Embeddings, and Attractors by : James C. Robinson

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.


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