Robinson, James C.  1969- <br/><br/>
Dimensions, embeddings, and attractors / 
James C. Robinson. 
 - Cambridge :  Cambridge University Press,  2011, p3s2011. 
 - xii, 205 pages :  illustrations ;  24 cm. 
 - Cambridge Tracts in Mathematics ;  186 .
 - Cambridge tracts in mathematics ;  186. .
<br/><br/>Includes bibliographical references (p. 196-201) and index. 
<br/><br/>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. 
<br/><br/> "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"-- 
<br/><br/><label>ISBN: </label>9780521898058 (hardback) 0521898056 (hardback) 
<br/><br/><label>LCCN: </label>2010042726 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Dimension theory (Topology)<br/>Attractors (Mathematics)<br/>Topological imbeddings.
<br/><br/><label>LC Class. No.: </label>QA611.3  / .R63 2011 
<br/><br/><label>Dewey Class. No.: </label>515.39