Dimensions, Embeddings, and Attractors: (Cambridge Tracts in Mathematics)
By
James C. Robinson (Author)
Hardback
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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. Worked examples or Exercises; 5 Halftones, unspecified; 5 Line drawings, unspecified
About the Author
James C. Robinson is Professor of Mathematics at Warwick University.
More Details
- Contributor: James C. Robinson
- Imprint: Cambridge University Press
- ISBN13: 9780521898058
- Number of Pages: 218
- Packaged Dimensions: 160x235x20mm
- Packaged Weight: 450
- Format: Hardback
- Publisher: Cambridge University Press
- Release Date: 2010-12-16
- Series: Cambridge Tracts in Mathematics
- Binding: Hardback
- Biography: James C. Robinson is Professor of Mathematics at Warwick University.
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