Knots and links in three-dimensional flows:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York
Springer
[1997]
|
| Schriftenreihe: | Lecture notes in mathematics
1654 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 208 Seiten Diagramme |
| ISBN: | 354062628X |
Internformat
MARC
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| 245 | 1 | 0 | |a Knots and links in three-dimensional flows |c Robert W. Ghrist ; Philip J. Holmes ; Michael C. Sullivan |
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer |c [1997] | |
| 264 | 4 | |c © 1997 | |
| 300 | |a X, 208 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1654 | |
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Datensatz im Suchindex
| _version_ | 1804125702620971008 |
|---|---|
| adam_text | Contents
0 Introduction 1
0.1 The contents of this volume 3
1 Prerequisites 5
1.1 The theory of knots and links 5
1.1.1 Basic definitions 5
1.1.2 New knots from old 8
1.1.3 Braid theory 10
1.1.4 Numerical invariants 12
1.2 The theory of dynamical systems 16
1.2.1 Basic definitions 16
1.2.2 Symbolic dynamics 22
1.2.3 Bifurcations and one dimensional maps 28
2 Templates 33
2.1 Branched manifolds and attractors 34
2.2 Templates and the Template Theorem 37
2.2.1 Case 1: a Markov flowbox neighborhood 39
2.2.2 Case 2: the DA 42
2.3 Examples and applications 47
2.3.1 The Lorenz like templates 47
2.3.2 Nonlinear oscillators, horseshoes, and Henon maps .... 49
2.3.3 Shil nikov connections 51
2.3.4 Fibred knots and links 54
2.3.5 Templates from time series 57
2.4 A symbolic language 60
2.4.1 Markov structures and symbolic coordinates 60
2.4.2 Subtemplates and template inflations 63
3 Template Theory 69
3.1 Knotted orbits on templates 69
3.1.1 Alexander s Theorem for templates 69
3.1.2 Concatenation of template knots 70
3.1.3 The existence of knots on a template 73
3.1.4 Accumulations of knots 75
3.2 Universal templates 78
3.2.1 Examples of subtemplate structures 78
3.2.2 A template containing all links 83
3.2.3 Universal templates 89
X CONTENTS
3.2.4 Where do all the knots live? 95
3.3 Subtemplate structures 97
3.3.1 Orientable subtemplates 98
3.3.2 Nonorientable subtemplates 103
4 Bifurcations 107
4.1 Local bifurcations and links 108
4.2 Torus knots and bifurcation sequences 112
4.2.1 Horseshoe torus knots 115
4.2.2 Bifurcation reversal in the Henon map 119
4.3 Self similarity and horseshoe cables 121
4.3.1 Kneading factorization and subtemplates 122
4.3.2 Nested periodic orbits and iterated torus knots 127
4.4 Homoclinic bifurcations 129
4.4.1 Gluing and torus knots 129
4.4.2 Silnikov connections and universal templates 134
5 Invariants 143
5.1 Classifying suspended subshifts 145
5.1.1 Finitely generated Abelian groups 148
5.2 Orientation data and stronger invariants 149
5.2.1 Additional examples 152
5.3 Zeta functions and flows 154
5.3.1 Review of zeta functions 154
5.3.2 Positive ribbons 155
5.3.3 Counting twisted ribbons 157
5.4 A zeta function for Lorenz attractors 159
5.5 Remarks on other invariants and open problems 165
6 Concluding Remarks 167
A Morse Smale / Smale Flows 171
A.I Morse Smale flows 171
A.1.1 Round handles 173
A.1.2 The3 sphere 175
A.1.3 Wada s Theorem 178
A.1.4 Extensions and applications 180
A.2 Smale flows, abstract 181
A.3 Smale flows, embedded 185
A.3.1 Lorenz templates 188
Bibliography 192
Index 205
|
| any_adam_object | 1 |
| author | Ghrist, Robert W. 1969- Holmes, Philip 1945- Sullivan, Michael C. |
| author_GND | (DE-588)1248893670 (DE-588)1058917994 (DE-588)1248894162 |
| author_facet | Ghrist, Robert W. 1969- Holmes, Philip 1945- Sullivan, Michael C. |
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| discipline | Mathematik |
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| id | DE-604.BV011205615 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:05:46Z |
| institution | BVB |
| isbn | 354062628X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007516211 |
| oclc_num | 246275199 |
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| physical | X, 208 Seiten Diagramme |
| publishDate | 1997 |
| publishDateSearch | 1997 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Ghrist, Robert W. 1969- (DE-588)1248893670 aut Knots and links in three-dimensional flows Robert W. Ghrist ; Philip J. Holmes ; Michael C. Sullivan Berlin ; Heidelberg ; New York Springer [1997] © 1997 X, 208 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1654 Flows (Differentiable dynamical systems) Knot theory Link theory Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Verschlingung (DE-588)4191540-9 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dreidimensionale Strömung (DE-588)4150635-2 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Verschlingung (DE-588)4191540-9 s Knoten Mathematik (DE-588)4164314-8 s DE-604 Dreidimensionale Strömung (DE-588)4150635-2 s Holmes, Philip 1945- (DE-588)1058917994 aut Sullivan, Michael C. (DE-588)1248894162 aut Erscheint auch als Online-Ausgabe 978-3-540-68347-6 Lecture notes in mathematics 1654 (DE-604)BV000676446 1654 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007516211&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ghrist, Robert W. 1969- Holmes, Philip 1945- Sullivan, Michael C. Knots and links in three-dimensional flows Lecture notes in mathematics Flows (Differentiable dynamical systems) Knot theory Link theory Knoten Mathematik (DE-588)4164314-8 gnd Verschlingung (DE-588)4191540-9 gnd Dynamisches System (DE-588)4013396-5 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dreidimensionale Strömung (DE-588)4150635-2 gnd Dimension 3 (DE-588)4321722-9 gnd |
| subject_GND | (DE-588)4164314-8 (DE-588)4191540-9 (DE-588)4013396-5 (DE-588)4037379-4 (DE-588)4150635-2 (DE-588)4321722-9 |
| title | Knots and links in three-dimensional flows |
| title_auth | Knots and links in three-dimensional flows |
| title_exact_search | Knots and links in three-dimensional flows |
| title_full | Knots and links in three-dimensional flows Robert W. Ghrist ; Philip J. Holmes ; Michael C. Sullivan |
| title_fullStr | Knots and links in three-dimensional flows Robert W. Ghrist ; Philip J. Holmes ; Michael C. Sullivan |
| title_full_unstemmed | Knots and links in three-dimensional flows Robert W. Ghrist ; Philip J. Holmes ; Michael C. Sullivan |
| title_short | Knots and links in three-dimensional flows |
| title_sort | knots and links in three dimensional flows |
| topic | Flows (Differentiable dynamical systems) Knot theory Link theory Knoten Mathematik (DE-588)4164314-8 gnd Verschlingung (DE-588)4191540-9 gnd Dynamisches System (DE-588)4013396-5 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Dreidimensionale Strömung (DE-588)4150635-2 gnd Dimension 3 (DE-588)4321722-9 gnd |
| topic_facet | Flows (Differentiable dynamical systems) Knot theory Link theory Knoten Mathematik Verschlingung Dynamisches System Mannigfaltigkeit Dreidimensionale Strömung Dimension 3 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007516211&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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