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portada dimensions, embeddings, and attractors
dimensions, embeddings, and attractorsdimensions, embeddings, and attractorsdimensions, embeddings, and attractors
Type
Physical Book
Author
Publisher
Year
2011
Language
English
Pages
205
Format
Hardcover
Dimensions
22.9x15.2x2 cm
Weight
0.45 kg.
ISBN13
9780521898058
Categories

dimensions, embeddings, and attractors

James C. Robinson (Author) · Cambridge University Press · Hardcover

dimensions, embeddings, and attractors - Robinson, James C.

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Synopsis "dimensions, embeddings, and attractors"

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.

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