Morse theory of gradient flows, concavity and complexity on manifolds with boundary:
"This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth map...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Publishing
2019
|
| Schlagworte: | |
| Online-Zugang: | UBY01 URL des Erstveröffentlichers |
| Zusammenfassung: | "This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps. The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it. The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters"--Publisher's website |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader |
| Beschreibung: | 1 online resource (xvi, 497 pages) illustrations |
| ISBN: | 9789814368766 9814368768 |
Internformat
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| 100 | 1 | |a Katz, Gabriel |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Morse theory of gradient flows, concavity and complexity on manifolds with boundary |c Gabriel Katz |
| 264 | 1 | |a Singapore |b World Scientific Publishing |c 2019 | |
| 300 | |a 1 online resource (xvi, 497 pages) |b illustrations | ||
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| 500 | |a Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader | ||
| 505 | 8 | |a Includes bibliographical references | |
| 505 | 8 | |a Preface - Acknowledgments -- Flows in 2D and 3D. A prelude in 2D: flows in flatland ; Vector fields, Morse stratifications, and gradient spines of 3-folds ; Concavity and complexity of traversing flows on 3-folds ; Deformations of traversing flows in 3d and modifications of gradient spines -- High-dimensional flows. Stratified convexity and concavity of flows on manifolds with boundary ; Traversally generic and versal flows: semi-algebraic models of tangency ; Combinatorics of tangency: the stratified spaces of real polynomials ; Complexity of shadows and traversing flows in terms of the simplicial volume ; The burnside ring-valued Morse formula for equivariant vector fields | |
| 520 | |a "This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps. The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it. The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters"--Publisher's website | ||
| 650 | 4 | |a Differentiable manifolds | |
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Datensatz im Suchindex
| _version_ | 1804181612570607616 |
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| adam_txt | |
| any_adam_object | |
| any_adam_object_boolean | |
| author | Katz, Gabriel |
| author_facet | Katz, Gabriel |
| author_role | aut |
| author_sort | Katz, Gabriel |
| author_variant | g k gk |
| building | Verbundindex |
| bvnumber | BV046808794 |
| classification_rvk | SK 350 |
| collection | ZDB-124-WOP |
| contents | Includes bibliographical references Preface - Acknowledgments -- Flows in 2D and 3D. A prelude in 2D: flows in flatland ; Vector fields, Morse stratifications, and gradient spines of 3-folds ; Concavity and complexity of traversing flows on 3-folds ; Deformations of traversing flows in 3d and modifications of gradient spines -- High-dimensional flows. Stratified convexity and concavity of flows on manifolds with boundary ; Traversally generic and versal flows: semi-algebraic models of tangency ; Combinatorics of tangency: the stratified spaces of real polynomials ; Complexity of shadows and traversing flows in terms of the simplicial volume ; The burnside ring-valued Morse formula for equivariant vector fields |
| ctrlnum | (ZDB-124-WOP)00008282 (OCoLC)1190674622 (DE-599)BVBBV046808794 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV046808794 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:58:22Z |
| indexdate | 2024-07-10T08:54:25Z |
| institution | BVB |
| isbn | 9789814368766 9814368768 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032217396 |
| oclc_num | 1190674622 |
| open_access_boolean | |
| owner | DE-706 |
| owner_facet | DE-706 |
| physical | 1 online resource (xvi, 497 pages) illustrations |
| psigel | ZDB-124-WOP |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | World Scientific Publishing |
| record_format | marc |
| spelling | Katz, Gabriel Verfasser aut Morse theory of gradient flows, concavity and complexity on manifolds with boundary Gabriel Katz Singapore World Scientific Publishing 2019 1 online resource (xvi, 497 pages) illustrations txt rdacontent c rdamedia cr rdacarrier Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references Preface - Acknowledgments -- Flows in 2D and 3D. A prelude in 2D: flows in flatland ; Vector fields, Morse stratifications, and gradient spines of 3-folds ; Concavity and complexity of traversing flows on 3-folds ; Deformations of traversing flows in 3d and modifications of gradient spines -- High-dimensional flows. Stratified convexity and concavity of flows on manifolds with boundary ; Traversally generic and versal flows: semi-algebraic models of tangency ; Combinatorics of tangency: the stratified spaces of real polynomials ; Complexity of shadows and traversing flows in terms of the simplicial volume ; The burnside ring-valued Morse formula for equivariant vector fields "This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps. The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it. The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters"--Publisher's website Differentiable manifolds Vector bundles Morse-Theorie (DE-588)4197103-6 gnd rswk-swf Electronic books Morse-Theorie (DE-588)4197103-6 s DE-604 Erscheint auch als Druck-Ausgabe 9789814368759 Erscheint auch als Druck-Ausgabe 981436875X https://www.worldscientific.com/worldscibooks/10.1142/8282 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Katz, Gabriel Morse theory of gradient flows, concavity and complexity on manifolds with boundary Includes bibliographical references Preface - Acknowledgments -- Flows in 2D and 3D. A prelude in 2D: flows in flatland ; Vector fields, Morse stratifications, and gradient spines of 3-folds ; Concavity and complexity of traversing flows on 3-folds ; Deformations of traversing flows in 3d and modifications of gradient spines -- High-dimensional flows. Stratified convexity and concavity of flows on manifolds with boundary ; Traversally generic and versal flows: semi-algebraic models of tangency ; Combinatorics of tangency: the stratified spaces of real polynomials ; Complexity of shadows and traversing flows in terms of the simplicial volume ; The burnside ring-valued Morse formula for equivariant vector fields Differentiable manifolds Vector bundles Morse-Theorie (DE-588)4197103-6 gnd |
| subject_GND | (DE-588)4197103-6 |
| title | Morse theory of gradient flows, concavity and complexity on manifolds with boundary |
| title_auth | Morse theory of gradient flows, concavity and complexity on manifolds with boundary |
| title_exact_search | Morse theory of gradient flows, concavity and complexity on manifolds with boundary |
| title_exact_search_txtP | Morse theory of gradient flows, concavity and complexity on manifolds with boundary |
| title_full | Morse theory of gradient flows, concavity and complexity on manifolds with boundary Gabriel Katz |
| title_fullStr | Morse theory of gradient flows, concavity and complexity on manifolds with boundary Gabriel Katz |
| title_full_unstemmed | Morse theory of gradient flows, concavity and complexity on manifolds with boundary Gabriel Katz |
| title_short | Morse theory of gradient flows, concavity and complexity on manifolds with boundary |
| title_sort | morse theory of gradient flows concavity and complexity on manifolds with boundary |
| topic | Differentiable manifolds Vector bundles Morse-Theorie (DE-588)4197103-6 gnd |
| topic_facet | Differentiable manifolds Vector bundles Morse-Theorie |
| url | https://www.worldscientific.com/worldscibooks/10.1142/8282 |
| work_keys_str_mv | AT katzgabriel morsetheoryofgradientflowsconcavityandcomplexityonmanifoldswithboundary |