Dimensions, embeddings, and attractors / (Record no. 518279)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03080nam a22003858i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511933912 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160238.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 100928s2011||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511933912 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521898058 (hardback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA611.3 |
| Item number | .R63 2011 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.39 |
| Edition number | 22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Robinson, James C. |
| Fuller form of name | (James Cooper), |
| Dates associated with a name | 1969- |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Dimensions, embeddings, and attractors / |
| Statement of responsibility, etc | James C. Robinson. |
| 246 3# - VARYING FORM OF TITLE | |
| Title proper/short title | Dimensions, Embeddings, & Attractors |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2011. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xii, 205 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| სერიის ცნობა | Cambridge tracts in mathematics ; |
| Volume number/sequential designation | 186 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Dimension theory (Topology) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Attractors (Mathematics) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Topological imbeddings. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9780521898058 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Cambridge tracts in mathematics ; |
| Volume number/sequential designation | 186. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511933912">https://doi.org/10.1017/CBO9780511933912</a> |
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