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Item Details
| Title:
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DIMENSIONS, EMBEDDINGS, AND ATTRACTORS
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| By: |
James C. Robinson |
| Format: |
Electronic book text |
| List price:
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£102.00 |
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further information.
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| ISBN 10: |
0511933916 |
| ISBN 13: |
9780511933912 |
| Publisher: |
CAMBRIDGE UNIVERSITY PRESS |
| Pub. date: |
10 January, 2011 |
| Series: |
Cambridge Tracts in Mathematics 186 |
| Description: |
Accessible monograph exploring what it means for a set to be 'finite-dimensional' and applying the abstract theory to attractors. |
| Synopsis: |
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. |
| Illustrations: |
10 b/w illus. 60 exercises |
| Publication: |
UK |
| Imprint: |
Cambridge University Press (Virtual Publishing) |
| Returns: |
Non-returnable |
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