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Dimensions, Embeddings, and Attractors, Hardback Book

Dimensions, Embeddings, and Attractors Hardback

Part of the Cambridge Tracts in Mathematics series

Description

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.

Information

  • Format: Hardback
  • Pages: 218 pages, Worked examples or Exercises; 5 Halftones, unspecified; 5 Line drawings, unspecified
  • Publisher: Cambridge University Press
  • Publication Date:
  • Category: Functional analysis & transforms
  • ISBN: 9780521898058

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