Dimensions, embeddings, and attractors
By: by James C. Robinson
Series: Cambridge tracts in mathematics -- 186
Publisher: Cambridge University Press
Published: 2011
Place of publication: Cambridge
Language: eng
Number of pages: 205
ISBN-13: 9780521898058
Subjects: Attractors (Mathematics); Topological imbeddings; Dimension theory (Topology); Differentiable dynamical systems
Description: "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"--