Dimensions, Embeddings, and Attractors

English

Series: Cambridge Tracts in Mathematics Ser.

ISBN: 0511924453

EAN: 9780511924453

Category: Mathematics / Differential Equations

Publisher: Cambridge University Press

Release Date: 12/31/2010

Synopsis: 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.

Excerpt: Unknown Property Excerpt

Dimensions, Embeddings, and Attractors

Illustrated: No

Format: eBook - PDF

Pages: 225