02887cam a22003254a 450000100090000000300040000900500170001300800410003001000170007102000290008802000260011703500240014304000600016704200080022705000230023508200150025810000470027324500650032026000610038530000460044649000430049250400640053550506820059952010630128165000320234465000290237665000280240583000440243385600840247716488986OSt20150408114025.0101004t20112011enka     b    001 0 eng    a  2010042726  a9780521898058 (hardback)  a0521898056 (hardback)  a(OCoLC)ocn676062809  aDLCerdacDLCdYDXdNUIdYDXCPdCDXdBWXdUMSdIXAdDLC  apcc00aQA611.3b.R63 201100a515.392221 aRobinson, James C.q(James Cooper),d1969-10aDimensions, embeddings, and attractors /cJames C. Robinson.  aCambridge :bCambridge University Press,c2011, p3s2011.  axii, 205 pages :billustrations ;c24 cm.1 aCambridge Tracts in Mathematics ;v186  aIncludes bibliographical references (p. 196-201) and index.0 aFinite-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.  a"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"-- 0aDimension theory (Topology) 0aAttractors (Mathematics) 0aTopological imbeddings. 0aCambridge tracts in mathematics ;v186.423Cover imageuhttp://assets.cambridge.org/97805218/98058/cover/9780521898058.jpg