Dimensions, Embeddings, and Attractors (Cambridge Tracts in Mathematics, Series Number 186) free ebook download.

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Dimensions, Embeddings, and Attractors (Cambridge Tracts in Mathematics, Series Number 186) free ebook download

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Mathematics

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Date:	2021	Format:	pdf	Language:	English	ISBN/ASIN:	0521898056
Pages:	218	OCR:		Quality:		ISBN13:
Uploader:	risotor	Upload Date:	9/28/2022 3:29:50 AM

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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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Tags: Attractors Cambridge Dimensions Embeddings Mathematics Number Tracts

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