Theory of degrees with applications to bifurcations and differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1997
|
| Schriftenreihe: | Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts
[17] |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 374 S. graph. Darst. |
| ISBN: | 0471157406 |
Internformat
MARC
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| 100 | 1 | |a Krawcewicz, Wieslaw |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Theory of degrees with applications to bifurcations and differential equations |c Wieslaw Krawcewicz ; Jianhong Wu |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1997 | |
| 300 | |a XIV, 374 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts |v [17] | |
| 650 | 4 | |a Bifurcation theory | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Topological degree | |
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| 700 | 1 | |a Wu, Jianhong |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804125727629508608 |
|---|---|
| adam_text | Contents
Preface ix
Introduction xiii
Chapter 1 Elements of Differential Topology 1
1.1 Differential Manifolds and Submanifolds 1
1.2 Differentiate Maps, Lie Groups, and Tangent Bundles 6
1.3 Embeddings, Immersions, and Transversality 15
1.4 Vector Bundles 25
1.5 Elements of Homotopy Theory 32
1.6 Bibliographical Notes 40
Chapter 2 Degree in Finite Dimensional Spaces 41
2.1 Axioms and Basic Properties 41
2.2 Computation of the Degree 45
2.3 Construction of the Degree 51
2.4 Further Properties of the Degree 56
2.5 Application: Existence of Equilibria in Differential
Equations 63
2.6 Bibliographical Notes 65
Chapter 3 Leray Schauder Degree for Compact Fields 66
3.1 Schauder s Approximations and Leray Schauder Degree 68
3.2 Fixed Point Theorems 80
3.3 Compact Linear Operators 83
3.4 Application: Bernstein s Theorem for BVPs 87
3.5 Application: Nonlinear BVPs 91
3.6 A Fixed Point Index for ENRs and ANRs 96
3.7 Bibliographical Notes 100
Chapter 4 Nussbaum Sadovskii Degree for Condensing Fields 102
4.1 Measure of Noncompactness and Condensing Mappings 102
4.2 Construction and Application of Nussbaum Sadovskii
Degree 110
vii
viii Contents
4.3 Other Properties of Condensing Fields 116
4.4 Regular Value Formula for Condensing Fields 124
4.5 Application: BVPs of Neutral Equations 135
4.6 Composite Coincidence Degree 150
4.7 Application: Periodic Solutions of Neutral Equations 157
4.8 Bibliographical Notes 164
Chapter 5 Applications to Bifurcation Theory 166
5.1 Local Bifurcation Theory 166
5.2 Global Bifurcation Theory 172
5.3 Application: Sturm Liouville Problems 178
5.4 Bibliographical Notes 182
Chapter 6 S1 Equivariant Degree 184
6.1 Elements of Representation Theory 184
6.2 Equivariant Normal Approximations 204
6.3 Construction of 5 Equivariant Degree 213
6.4 S1 Equivariant Degree in Infinite Dimensional Spaces 231
6.5 Bibliographical Notes 239
Chapter 7 Global Hopf Bifurcation Theory 240
7.1 Hopf Bifurcation for Composite Coincidence Problems 240
7.2 Global Hopf Bifurcation Theory of Neutral Equations 251
7.3 Global Continuation of Periodic Solutions: An Example 266
7.4 Bibliographical Notes 281
Chapter 8 Equivariant Degree of Dold UInch 282
8.1 Preliminaries on G actions 282
8.2 Burnside Ring A{G) 288
8.3 Normal Approximations and G Degree of Dold Ulrich 300
8.4 Examples of Computations of G Degree 314
8.5 G Equivariant Bifurcation Problems 327
8.6 Periodic Solutions of Time Reversible Functional Systems 332
8.7 Branching Lemma for Equivariant Bifurcations 340
8.8 Steady State Bifurcation: Spontaneous Symmetry Breaking 352
8.9 Bibliographical Notes 356
References 357
Index 369
|
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| author | Krawcewicz, Wieslaw Wu, Jianhong |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.355 |
| dewey-search | 515/.355 |
| dewey-sort | 3515 3355 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011228133 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:06:09Z |
| institution | BVB |
| isbn | 0471157406 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007534149 |
| oclc_num | 70452500 |
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| physical | XIV, 374 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Wiley |
| record_format | marc |
| series | Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts |
| series2 | Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts |
| spelling | Krawcewicz, Wieslaw Verfasser aut Theory of degrees with applications to bifurcations and differential equations Wieslaw Krawcewicz ; Jianhong Wu New York [u.a.] Wiley 1997 XIV, 374 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts [17] Bifurcation theory Differential equations Topological degree Abbildung Mathematik (DE-588)4000044-8 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Abbildungsgrad (DE-588)4140975-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Abbildung Mathematik (DE-588)4000044-8 s Abbildungsgrad (DE-588)4140975-9 s DE-604 Wu, Jianhong Verfasser aut Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts [17] (DE-604)BV012067942 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007534149&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krawcewicz, Wieslaw Wu, Jianhong Theory of degrees with applications to bifurcations and differential equations Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts Bifurcation theory Differential equations Topological degree Abbildung Mathematik (DE-588)4000044-8 gnd Differentialgleichung (DE-588)4012249-9 gnd Abbildungsgrad (DE-588)4140975-9 gnd |
| subject_GND | (DE-588)4000044-8 (DE-588)4012249-9 (DE-588)4140975-9 |
| title | Theory of degrees with applications to bifurcations and differential equations |
| title_auth | Theory of degrees with applications to bifurcations and differential equations |
| title_exact_search | Theory of degrees with applications to bifurcations and differential equations |
| title_full | Theory of degrees with applications to bifurcations and differential equations Wieslaw Krawcewicz ; Jianhong Wu |
| title_fullStr | Theory of degrees with applications to bifurcations and differential equations Wieslaw Krawcewicz ; Jianhong Wu |
| title_full_unstemmed | Theory of degrees with applications to bifurcations and differential equations Wieslaw Krawcewicz ; Jianhong Wu |
| title_short | Theory of degrees with applications to bifurcations and differential equations |
| title_sort | theory of degrees with applications to bifurcations and differential equations |
| topic | Bifurcation theory Differential equations Topological degree Abbildung Mathematik (DE-588)4000044-8 gnd Differentialgleichung (DE-588)4012249-9 gnd Abbildungsgrad (DE-588)4140975-9 gnd |
| topic_facet | Bifurcation theory Differential equations Topological degree Abbildung Mathematik Differentialgleichung Abbildungsgrad |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007534149&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012067942 |
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