bokomslag Dimensions, Embeddings, and Attractors
Vetenskap & teknik

Dimensions, Embeddings, and Attractors

James C Robinson

Inbunden

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  • 218 sidor
  • 2010
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.
  • Författare: James C Robinson
  • Format: Inbunden
  • ISBN: 9780521898058
  • Språk: Engelska
  • Antal sidor: 218
  • Utgivningsdatum: 2010-12-16
  • Förlag: Cambridge University Press