000			03125cam a22003614a 4500
001			16488986
003			OSt
005			20150408114025.0
008			101004t20112011enka b 001 0 eng
010			_a 2010042726
020			_a9780521898058 (hardback)
020			_a0521898056 (hardback)
035			_a(OCoLC)ocn676062809
040			_aDLC _erda _cDLC _dYDX _dNUI _dYDXCP _dCDX _dBWX _dUMS _dIXA _dDLC
042			_apcc
050	0	0	_aQA611.3 _b.R63 2011
082	0	0	_a515.39 _222
100	1		_aRobinson, James C. _q(James Cooper), _d1969- _914532
245	1	0	_aDimensions, embeddings, and attractors / _cJames C. Robinson.
260			_aCambridge : _bCambridge University Press, _c2011, p3s2011.
300			_axii, 205 pages : _billustrations ; _c24 cm.
490	1		_aCambridge Tracts in Mathematics ; _v186
504			_aIncludes bibliographical references (p. 196-201) and index.
505	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.
520			_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"--
650		0	_aDimension theory (Topology) _914533
650		0	_aAttractors (Mathematics) _98856
650		0	_aTopological imbeddings. _914534
830		0	_aCambridge tracts in mathematics ; _v186. _914535
856	4	2	_3Cover image _uhttp://assets.cambridge.org/97805218/98058/cover/9780521898058.jpg
942			_2ddc _cBOOK
999			_c22292 _d256792