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    3. Dimensions, Embeddings, and Attractors

    Dimensions, Embeddings, and Attractors

    Posted By: arundhati
    Date: 27 May 2014 05:14:44
    Dimensions, Embeddings, and Attractors

    James C. Robinson, "Dimensions, Embeddings, and Attractors"
    2011 | ISBN-10: 0521898056 | 218 pages | PDF | 1 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 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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