Analytic theory of global bifurcation: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, N.J.
Princeton University Press
2003
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| Series: | Princeton series in applied mathematics
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| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | X, 169 S. graph. Darst. |
| ISBN: | 0691112983 |
Staff View
MARC
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| 100 | 1 | |a Buffoni, Boris |d 1965- |e Verfasser |0 (DE-588)1146433263 |4 aut | |
| 245 | 1 | 0 | |a Analytic theory of global bifurcation |b an introduction |c Boris Buffoni and John Toland |
| 264 | 1 | |a Princeton, N.J. |b Princeton University Press |c 2003 | |
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| 490 | 0 | |a Princeton series in applied mathematics | |
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 7 | |a Bifurcatie |2 gtt | |
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| 650 | 7 | |a Differentiaalvergelijkingen |2 gtt | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Chapter 1. Introduction 1
1.1 Example: Bending an Elastic Rod I 2
1.2 Principle of Linearization 5
1.3 Global Theory 6
1.4 Layout 7
PART 1. LINEAR AND NONLINEAR
FUNCTIONAL ANALYSIS 9
Chapter 2. Linear Functional Analysis 11
2.1 Preliminaries and Notation 11
2.2 Subspaces 13
2.3 Dual Spaces 14
2.4 Linear Operators 15
2.5 Neumann Series 16
2.6 Projections and Subspaces 17
2.7 Compact and Fredholm Operators 18
2.8 Notes on Sources 20
Chapter 3. Calculus in Banach Spaces 21
3.1 Frechet Differentiation 21
3.2 Higher Derivatives 27
3.3 Taylor s Theorem 31
3.4 Gradient Operators 32
3.5 Inverse and Implicit Function Theorems 35
3.6 Perturbation of a Simple Eigenvalue 38
3.7 Notes on Sources 40
Chapter 4. Multilinear and Analytic Operators 41
4.1 Bounded Multilinear Operators 41
4.2 Faa de Bruno Formula 44
4.3 Analytic Operators 45
4.4 Analytic Functions of Two Variables 52
Vi CONTENTS
4.5 Analytic Inverse and Implicit
Function Theorems 53
4.6 Notes on Sources 57
PART 2. ANALYTIC VARIETIES 59
Chapter 5. Analytic Functions on Fn 61
5.1 Preliminaries 61
5.2 Weierstrass Division Theorem 64
5.3 Weierstrass Preparation Theorem 65
5.4 Riemann Extension Theorem 66
5.5 Notes on Sources 69
Chapter 6. Polynomials 70
6.1 Constant Coefficients 70
6.2 Variable Coefficients 74
6.3 Notes on Sources 77
Chapter 7. Analytic Varieties 78
7.1 F Analytic Varieties 78
7.2 Weierstrass Analytic Varieties 81
7.3 Analytic Germs and Subspaces 86
7.4 Germs of C analytic Varieties 88
7.5 One dimensional Branches 95
7.6 Notes on Sources 99
PART 3. BIFURCATION THEORY 101
Chapter 8. Local Bifurcation Theory 103
8.1 A Necessary Condition 103
8.2 Lyapunov Schmidt Reduction 104
8.3 Crandall Rabinowitz Transversality 105
8.4 Bifurcation from a Simple Eigenvalue 109
8.5 Bending an Elastic Rod II 111
8.6 Bifurcation of Periodic Solutions 112
8.7 Notes on Sources 113
Chapter 9. Global Bifurcation Theory 114
9.1 Global One Dimensional Branches 114
9.2 Global Analytic Bifurcation in Cones 120
9.3 Bending an Elastic Rod III 121
9.4 Notes on Sources 124
CONTENTS Vii
PART 4. STOKES WAVES 125
Chapter 10. Steady Periodic Water Waves 127
10.1 Euler Equations 127
10.2 One dimensional Formulation 131
10.3 Main Equation 137
10.4 A Priori Bounds and Nekrasov s Equation 140
10.5 Weak Solutions Are Classical 146
10.6 Notes on Sources 151
Chapter 11. Global Existence of Stokes Waves 152
11.1 Local Bifurcation Theory 152
11.2 Global Bifurcation from A = 1 154
11.3 Gradients, Morse Index and Bifurcation 157
11.4 Notes on Sources 159
Bibliography 161
Index 167
|
| any_adam_object | 1 |
| author | Buffoni, Boris 1965- |
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| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:08:44Z |
| institution | BVB |
| isbn | 0691112983 |
| language | English |
| lccn | 2002192482 |
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| physical | X, 169 S. graph. Darst. |
| publishDate | 2003 |
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| spelling | Buffoni, Boris 1965- Verfasser (DE-588)1146433263 aut Analytic theory of global bifurcation an introduction Boris Buffoni and John Toland Princeton, N.J. Princeton University Press 2003 X, 169 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Princeton series in applied mathematics Includes bibliographical references and index Analytische functies gtt Análise global larpcal Bifurcatie gtt Bifurcation, Théorie de la Differentiaalvergelijkingen gtt Teoria da bifurcação (equações diferenciais) larpcal Bifurcation theory Globale Verzweigung (DE-588)4374566-0 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Globale Verzweigung (DE-588)4374566-0 s Funktionalanalysis (DE-588)4018916-8 s DE-604 Toland, John F. 1949- Sonstige (DE-588)137934033 oth http://www.loc.gov/catdir/description/prin031/2002192482.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010080147&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buffoni, Boris 1965- Analytic theory of global bifurcation an introduction Analytische functies gtt Análise global larpcal Bifurcatie gtt Bifurcation, Théorie de la Differentiaalvergelijkingen gtt Teoria da bifurcação (equações diferenciais) larpcal Bifurcation theory Globale Verzweigung (DE-588)4374566-0 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4374566-0 (DE-588)4018916-8 |
| title | Analytic theory of global bifurcation an introduction |
| title_auth | Analytic theory of global bifurcation an introduction |
| title_exact_search | Analytic theory of global bifurcation an introduction |
| title_full | Analytic theory of global bifurcation an introduction Boris Buffoni and John Toland |
| title_fullStr | Analytic theory of global bifurcation an introduction Boris Buffoni and John Toland |
| title_full_unstemmed | Analytic theory of global bifurcation an introduction Boris Buffoni and John Toland |
| title_short | Analytic theory of global bifurcation |
| title_sort | analytic theory of global bifurcation an introduction |
| title_sub | an introduction |
| topic | Analytische functies gtt Análise global larpcal Bifurcatie gtt Bifurcation, Théorie de la Differentiaalvergelijkingen gtt Teoria da bifurcação (equações diferenciais) larpcal Bifurcation theory Globale Verzweigung (DE-588)4374566-0 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Analytische functies Análise global Bifurcatie Bifurcation, Théorie de la Differentiaalvergelijkingen Teoria da bifurcação (equações diferenciais) Bifurcation theory Globale Verzweigung Funktionalanalysis |
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