Dimensions, embeddings, and attractors:
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 dis...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2011
|
| Schriftenreihe: | Cambridge tracts in mathematics
186 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | 1 Online-Ressource (xii, 205 Seiten) |
| ISBN: | 9780511933912 |
| DOI: | 10.1017/CBO9780511933912 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043942085 | ||
| 003 | DE-604 | ||
| 005 | 20190513 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s2011 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511933912 |c Online |9 978-0-511-93391-2 | ||
| 024 | 7 | |a 10.1017/CBO9780511933912 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511933912 | ||
| 035 | |a (OCoLC)839036967 | ||
| 035 | |a (DE-599)BVBBV043942085 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 |a DE-355 | ||
| 082 | 0 | |a 515/.39 |2 22 | |
| 084 | |a SK 300 |0 (DE-625)143230: |2 rvk | ||
| 100 | 1 | |a Robinson, James C. |d 1969- |e Verfasser |0 (DE-588)143220004 |4 aut | |
| 245 | 1 | 0 | |a Dimensions, embeddings, and attractors |c James C. Robinson |
| 246 | 1 | 3 | |a Dimensions, Embeddings, & Attractors |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2011 | |
| 300 | |a 1 Online-Ressource (xii, 205 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Cambridge tracts in mathematics |v 186 | |
| 505 | 8 | |a 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 | |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 | 4 | |a Dimension theory (Topology) | |
| 650 | 4 | |a Attractors (Mathematics) | |
| 650 | 4 | |a Topological imbeddings | |
| 650 | 0 | 7 | |a Dimensionstheorie |0 (DE-588)4149935-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Attraktor |0 (DE-588)4140563-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Topologische Einbettung |0 (DE-588)4455162-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Dimensionstheorie |0 (DE-588)4149935-9 |D s |
| 689 | 0 | 1 | |a Topologische Einbettung |0 (DE-588)4455162-9 |D s |
| 689 | 0 | 2 | |a Attraktor |0 (DE-588)4140563-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-0-521-89805-8 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511933912 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029351055 | ||
| 966 | e | |u https://doi.org/10.1017/CBO9780511933912 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511933912 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511933912 |l UBR01 |p ZDB-20-CBO |q UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176884526743552 |
|---|---|
| any_adam_object | |
| author | Robinson, James C. 1969- |
| author_GND | (DE-588)143220004 |
| author_facet | Robinson, James C. 1969- |
| author_role | aut |
| author_sort | Robinson, James C. 1969- |
| author_variant | j c r jc jcr |
| building | Verbundindex |
| bvnumber | BV043942085 |
| classification_rvk | SK 300 |
| collection | ZDB-20-CBO |
| contents | 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511933912 (OCoLC)839036967 (DE-599)BVBBV043942085 |
| dewey-full | 515/.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.39 |
| dewey-search | 515/.39 |
| dewey-sort | 3515 239 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511933912 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03915nmm a2200541zcb4500</leader><controlfield tag="001">BV043942085</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20190513 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s2011 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511933912</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-93391-2</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511933912</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511933912</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)839036967</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043942085</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield><subfield code="a">DE-355</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.39</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 300</subfield><subfield code="0">(DE-625)143230:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Robinson, James C.</subfield><subfield code="d">1969-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)143220004</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Dimensions, embeddings, and attractors</subfield><subfield code="c">James C. Robinson</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Dimensions, Embeddings, & Attractors</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xii, 205 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Cambridge tracts in mathematics</subfield><subfield code="v">186</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">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</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dimension theory (Topology)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Attractors (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topological imbeddings</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Dimensionstheorie</subfield><subfield code="0">(DE-588)4149935-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Attraktor</subfield><subfield code="0">(DE-588)4140563-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologische Einbettung</subfield><subfield code="0">(DE-588)4455162-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Dimensionstheorie</subfield><subfield code="0">(DE-588)4149935-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Topologische Einbettung</subfield><subfield code="0">(DE-588)4455162-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Attraktor</subfield><subfield code="0">(DE-588)4140563-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-0-521-89805-8</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511933912</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029351055</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511933912</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511933912</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511933912</subfield><subfield code="l">UBR01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">UBR Einzelkauf (Lückenergänzung CUP Serien 2018)</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043942085 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511933912 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351055 |
| oclc_num | 839036967 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xii, 205 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Robinson, James C. 1969- Verfasser (DE-588)143220004 aut Dimensions, embeddings, and attractors James C. Robinson Dimensions, Embeddings, & Attractors Cambridge Cambridge University Press 2011 1 Online-Ressource (xii, 205 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 186 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 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 Dimension theory (Topology) Attractors (Mathematics) Topological imbeddings Dimensionstheorie (DE-588)4149935-9 gnd rswk-swf Attraktor (DE-588)4140563-8 gnd rswk-swf Topologische Einbettung (DE-588)4455162-9 gnd rswk-swf Dimensionstheorie (DE-588)4149935-9 s Topologische Einbettung (DE-588)4455162-9 s Attraktor (DE-588)4140563-8 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-89805-8 https://doi.org/10.1017/CBO9780511933912 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Robinson, James C. 1969- Dimensions, embeddings, and attractors 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 Dimension theory (Topology) Attractors (Mathematics) Topological imbeddings Dimensionstheorie (DE-588)4149935-9 gnd Attraktor (DE-588)4140563-8 gnd Topologische Einbettung (DE-588)4455162-9 gnd |
| subject_GND | (DE-588)4149935-9 (DE-588)4140563-8 (DE-588)4455162-9 |
| title | Dimensions, embeddings, and attractors |
| title_alt | Dimensions, Embeddings, & Attractors |
| title_auth | Dimensions, embeddings, and attractors |
| title_exact_search | Dimensions, embeddings, and attractors |
| title_full | Dimensions, embeddings, and attractors James C. Robinson |
| title_fullStr | Dimensions, embeddings, and attractors James C. Robinson |
| title_full_unstemmed | Dimensions, embeddings, and attractors James C. Robinson |
| title_short | Dimensions, embeddings, and attractors |
| title_sort | dimensions embeddings and attractors |
| topic | Dimension theory (Topology) Attractors (Mathematics) Topological imbeddings Dimensionstheorie (DE-588)4149935-9 gnd Attraktor (DE-588)4140563-8 gnd Topologische Einbettung (DE-588)4455162-9 gnd |
| topic_facet | Dimension theory (Topology) Attractors (Mathematics) Topological imbeddings Dimensionstheorie Attraktor Topologische Einbettung |
| url | https://doi.org/10.1017/CBO9780511933912 |
| work_keys_str_mv | AT robinsonjamesc dimensionsembeddingsandattractors AT robinsonjamesc dimensionsembeddingsattractors |