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.

Accessible monograph exploring what it means for a set to be 'finite-dimensional' and applying the abstract theory to attractors.

About the Author
James C. Robinson is Professor of Mathematics at Warwick University.


Book Information
ISBN 9780521898058
Author James C. Robinson
Format Hardback
Page Count 218
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 450g
Dimensions(mm) 235mm * 160mm * 20mm