000			03080nam a22003858i 4500
001			CR9780511933912
003			UkCbUP
005			20200124160238.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			100928s2011||||enk o ||1 0|eng|d
020			_a9780511933912 (ebook)
020			_z9780521898058 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA611.3 _b.R63 2011
082	0	0	_a515/.39 _222
100	1		_aRobinson, James C. _q(James Cooper), _d1969- _eauthor.
245	1	0	_aDimensions, embeddings, and attractors / _cJames C. Robinson.
246	3		_aDimensions, Embeddings, & Attractors
264		1	_aCambridge : _bCambridge University Press, _c2011.
300			_a1 online resource (xii, 205 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v186
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
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			_aThis 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)
650		0	_aAttractors (Mathematics)
650		0	_aTopological imbeddings.
776	0	8	_iPrint version: _z9780521898058
830		0	_aCambridge tracts in mathematics ; _v186.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511933912
999			_c518279 _d518277