Robinson, James C. (James Cooper) 1969- creator text bibliography enk Cambridge Cambridge University Press 2011, p3s2011 2011 2011 monographic eng

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xii, 205 pages : illustrations ; 24 cm. "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"-- Finite-dimensional sets. Lebesgue covering dimension -- Hausdorff measure and Hausdorff dimension -- Box-counting dimension -- An embedding theorem for subsets of RN -- Prevalence, probe spaces, and a crucial inequality -- Embedding sets with dH(X-X) finite -- Thickness exponents -- Embedding sets of finite box-counting dimension -- Assouad dimension -- Finite-dimensional attractors. Partial differential equations and nonlinear semigroups -- Attracting sets in infinite-dimensional systems -- Bounding the box-counting dimension of attractors -- Thickness exponents of attractors -- The Takens time-delay embedding theorem -- Parametrisation of attractors via point values. James C. Robinson. Includes bibliographical references (p. 196-201) and index. Dimension theory (Topology) Attractors (Mathematics) Topological imbeddings QA611.3 .R63 2011 515.39 9780521898058 (hardback) 0521898056 (hardback) 2010042726 http://assets.cambridge.org/97805218/98058/cover/9780521898058.jpg http://assets.cambridge.org/97805218/98058/cover/9780521898058.jpg DLC 101004 20150408114025.0 16488986