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Dimensions, Embeddings, and Attractors by James C. Robinson

Dimensions, Embeddings, and Attractors

by James C. Robinson
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Book cover type: Hardcover
  • ISBN13: 9780521898058
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date: N/A
  • Pages: 218
  • Original Price: GBP 67.0
  • Language: English
  • Edition: N/A
  • Item Weight: 454 grams
  • BISAC Subject(s): Differential Equations / General

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.

Robinson, James C.: - James C. Robinson is Professor of Mathematics at Warwick University.

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