03125cam a22003614a 4500 16488986 OSt 20150408114025.0 101004t20112011enka b 001 0 eng 2010042726 9780521898058 (hardback) 0521898056 (hardback) (OCoLC)ocn676062809 DLC rda DLC YDX NUI YDXCP CDX BWX UMS IXA DLC pcc QA611.3 .R63 2011 515.39 22 Robinson, James C. (James Cooper), 1969- 14532 Dimensions, embeddings, and attractors / James C. Robinson. Cambridge : Cambridge University Press, 2011, p3s2011. xii, 205 pages : illustrations ; 24 cm. Cambridge Tracts in Mathematics ; 186 Includes bibliographical references (p. 196-201) and index. 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. "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"-- Dimension theory (Topology) 14533 Attractors (Mathematics) 8856 Topological imbeddings. 14534 Cambridge tracts in mathematics ; 186. 14535 Cover image http://assets.cambridge.org/97805218/98058/cover/9780521898058.jpg ddc BOOK 22292 256792 0 2013-03-10 0 0 515.39 R J D 2012-05-20 EMF 00086509 EMF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.39 R J D 2012-05-20 EMF 00086510 EMF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.39 R J D 2012-06-01 SZM 00086747 SZM 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.39 R J D 2012-06-01 SZM 00086748 SZM 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.39 R J D 2012-06-02 EZF 00087522 EZF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.39 R J D 2012-06-02 EZF 00087524 EZF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.39 R J D 2012-06-04 SHF 00088192 SHF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 515.39 R J D 2012-06-04 SHF 00088193 SHF 2013-03-10 00:00:00 BOOK ddc 0