9780521898058

Dimensions, Embeddings, and Attractors

Format: Hardcover

ISBN13: 9780521898058

Hardcover|9780521898058


Overview

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-13

9780521898058

ISBN-10

0521898056

Weight

0.99 Pounds

Dimensions

6.00 x 0.80 x 9.00 In

List Price

$86.99

Edition

1st Edition

Format

Hardcover

Language

English

Pages

218 pages

Publisher

Cambridge University Press

Published On

2010-12-16



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