Dimensions, embeddings, and attractors
Robinson, James C. (2011) Dimensions, embeddings, and attractors. Cambridge tracts in mathematics, Vol.186 . Cambridge ; New York: Cambridge University Press. ISBN 9780521898058Full text not available from this repository.
Official URL: http://webcat.warwick.ac.uk/record=b2341614~S1
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.
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Series Name:||Cambridge tracts in mathematics|
|Publisher:||Cambridge University Press|
|Place of Publication:||Cambridge ; New York|
|Number of Pages:||205|
|Access rights to Published version:||Restricted or Subscription Access|
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