Dimensions, Embeddings, and Attractors Hardback
Part of the Cambridge Tracts in Mathematics series
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.
- Format: Hardback
- Pages: 218 pages, Worked examples or Exercises; 5 Halftones, unspecified; 5 Line drawings, unspecified
- Publisher: Cambridge University Press
- Publication Date: 16/12/2010
- Category: Functional analysis & transforms
- ISBN: 9780521898058