Dimensions, Embeddings, and Attractors James C. Robinson

ISBN: 9780511924453

Published: December 8th 2010

ebook

225 pages


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Dimensions, Embeddings, and Attractors  by  James C. Robinson

Dimensions, Embeddings, and Attractors by James C. Robinson
December 8th 2010 | ebook | PDF, EPUB, FB2, DjVu, AUDIO, mp3, ZIP | 225 pages | ISBN: 9780511924453 | 8.61 Mb

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 fourMoreThis 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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