Methods of bifurcation theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1996
|
| Edition: | Corr. 2. printing |
| Series: | Grundlehren der mathematischen Wissenschaften
251 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 501 - 522 |
| Physical Description: | XV, 525 S. graph. Darst. |
| ISBN: | 3540906649 0387906649 |
Staff View
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Record in the Search Index
| _version_ | 1804125652490649600 |
|---|---|
| adam_text | SHUI-NEE CHOW JACK K. HALE METHODS OF BIFURCATION THEORY CORRECTED
SECOND PRINTING WITH 97 ILLUSTRATIONS SPRINGER CONTENTS PREFACE VII
CHAPTER 1 INTRODUCTION AND EXAMPLES 1 1.1. DEFINITION OF BIFURCATION
SURFACE 1 1.2. EXAMPLES WITH ONE PARAMETER 3 1.3. THE EULER-BERNOULLI
ROD 5 1.4. THE HOPF BIFURCATION 9 1.5. SOME GENERIC EXAMPLES 12 1.6.
DYNAMIC BIFURCATION 15 CHAPTER 2 ELEMENTS OF NONLINEAR ANALYSIS 19 2.1.
CALCULUS 19 2.2. LOCAL IMPLICIT FUNCTION THEOREM 24 2.3. GLOBAL IMPLICIT
FUNCTION THEOREM 27 2.4. ALTERNATIVE METHODS 30 2.5. EMBEDDING THEOREMS
34 2.6. WEIERSTRASS PREPARATION THEOREM 36 2.7. THE MALGRANGE
PREPARATION THEOREM 43 2.8. NEWTON POLYGON 45 2.9. MANIFOLDS AND
TRANSVERSALITY 51 2.10. SARD S THEOREM 54 2.11. TOPOLOGICAL DEGREE.
INDEX OF A VECTOR FIELD AND FIXED POINT INDEX 65 2.12.
LJUSTERNIK-SCHNIRELMAN THEORY IN W 78 2.13. BIBLIOGRAPHICAL NOTES 85
CHAPTER 3 APPLICATIONS OF THE IMPLICIT FUNCTION THEOREM 89 3.1.
EXISTENCE OF SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 89 3.2.
ADMISSIBLE CLASSES IN ORDINARY DIFFERENTIAL EQUATIONS 90 3.3. GLOBAL
BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS . 92 XII
CONTENTS 3.4. HOPF BIFURCATION THEOREM 98 3.5. LIAPUNOV CENTER THEOREM
99 3.6. STABLE AND UNSTABLE MANIFOLDS 102 3.7. THE HARTMAN-GROBMAN
THEOREM 112 3.8. AN ELLIPTIC PROBLEM 115 3.9. A HYPERBOLIC PROBLEM 116
3.10. BIBLIOGRAPHICAL NOTES 118 CHAPTER 4 VARIATIONAL METHOD 120 4.1.
INTRODUCTION 120 4.2. WEAK LOWER SEMICONTINUITY 120 4.3. MONOTONE
OPERATORS 129 4.4. CONDITION (C) 134 4.5. MINIMAX PRINCIPLE IN BANACH
SPACES 139 4.6. MOUNTAIN PASS THEOREM 145 4.7. PERIODIC SOLUTIONS OF A
SEMILINEAR WAVE EQUATION 147 4.8. LJUSTEMIK-SCHNIRELMAN THEORY ON BANACH
MANIFOLDS 152 4.9. STATIONARY WAVES 156 4.10. THE KRASNOSELSKI THEOREMS
162 4.11. VARIATIONAL PROPERTY OF BIFURCATION EQUATION 165 4.12.
LIAPUNOV CENTER THEOREM AT RESONANCE 167 4.13. BIBLIOGRAPHICAL NOTES 171
CHAPTER 5 THE LINEAR APPROXIMATION AND BIFURCATION 173 5.1. INTRODUCTION
173 5.2. EIGENVALUES OF * 174 5.3. EIGENVALUES OF (B,A) 179 5.4.
EIGENVALUES OF (B,A *..., A N ) 182 5.5. BIFURCATION FROM A SIMPLE
EIGENVALUE 191 5.6. APPLICATIONS OF SIMPLE EIGENVALUES 196 5.7.
BIFURCATION BASED ON THE LINEAR EQUATION 206 5.8. GLOBAL BIFURCATION 211
5.9. AN APPLICATION TO A DELAY DIFFERENTIAL EQUATION 214 5.10.
BIBLIOGRAPHICAL NOTES 218 CHAPTER 6 BIFURCATION WITH ONE DIMENSIONAL
NULL SPACE 220 6.1. INTRODUCTION 220 6.2. QUADRATIC NONLINEARITIES 222
6.3. APPLICATIONS 227 6.4. CUBIC NONLINEARITIES 231 6.5. APPLICATIONS
235 / CONTENTS XIII 6.6. BIFURCATION FROM KNOWN SOLUTIONS 238 6.7.
EFFECTS OF SYMMETRY 241 6.8. UNIVERSAL UNFOLDINGS 246 6.9.
BIBLIOGRAPHICAL NOTES 247 CHAPTER 7 BIFURCATION WITH HIGHER DIMENSIONAL
NULL SPACES 249 7.1. INTRODUCTION 249 7.2. THE QUADRATIC REVISITED 250
7.3. QUADRATIC NONLINEARITIES I 253 7.4. QUADRATIC NONLINEARITIES II 263
7.5. CUBIC NONLINEARITIES I 268 7.6. CUBIC NONLINEARITIES II 275 7.7.
CUBIC NONLINEARITIES III 280 7.8. BIBLIOGRAPHICAL NOTES 285 CHAPTER 8
SOME APPLICATIONS 290 8.1. INTRODUCTION 290 8.2. THE VON KAERMAEN
EQUATIONS 290 8.3. THE LINEARIZED PROBLEM 292 8.4. NONCRITICAL LENGTH
294 8.5. CRITICAL LENGTH 296 8.6. AN EXAMPLE IN CHEMICAL REACTIONS 300
8.7. THE DUFFING EQUATION WITH HARMONIC FORCING 307 8.8. BIBLIOGRAPHICAL
NOTES 315 CHAPTER 9 BIFURCATION NEAR EQUILIBRIUM 317 9.1. INTRODUCTION
317 9.2. CENTER MANIFOLDS 318 9.3. AUTONOMOUS CASE 329 9.4. PERIODIC
CASE 336 9.5. BIFURCATION FROM A FOCUS 341 9.6. BIBLIOGRAPHICAL NOTES
350 CHAPTER 10 BIFURCATION OF AUTONOMOUS PLANAR EQUATIONS 357 10.1.
INTRODUCTION 357 10.2. PERIODIC ORBIT 357 10.3. HOMOCLINIC ORBIT 361 XIV
CONTENTS 10.4. CLOSED CURVE WITH A SADDLE-NODE 368 10.5. REMARKS ON
STRUCTURAL STABILITY AND BIFURCATION 370 10.6. REMARKS ON INFINITE
DIMENSIONAL SYSTEMS AND TURBULENCE 373 10.7. BIBLIOGRAPHICAL NOTES 375
CHAPTER 11 BIFURCATION OF PERIODIC EQUATIONS 376 11.1. INTRODUCTION 376
11.2. PERIODIC ORBIT-SUBHARMONICS 377 11.3. HOMOCLINIC ORBIT 386 11.4.
SUBHARMONICS AND HOMOCLINIC POINTS 396 11.5. ABSTRACT BIFURCATION NEAR A
CLOSED CURVE 403 11.6. BIBLIOGRAPHICAL NOTES 405 CHAPTER 12 NORMAL FORMS
AND INVARIANT MANIFOLDS 409 12.1. INTRODUCTION 409 12.2. TRANSFORMATION
THEORY AND NORMAL FORMS 410 12.3. MORE ON NORMAL FORMS 418 12.4. THE
METHOD OF AVERAGING 428 12.5. INTEGRAL MANIFOLDS AND INVARIANT TORI 433
12.6. BIFURCATION FROM A PERIODIC ORBIT TO A TORUS 440 12.7. BIFURCATION
OF TORI 447 12.8. BIBLIOGRAPHICAL NOTES 449 CHAPTER 13 HIGHER ORDER
BIFURCATION NEAR EQUILIBRIUM 451 13.1. INTRODUCTION 451 13.2. TWO ZERO
ROOTS I 452 13.3. TWO ZERO ROOTS II 458 13.4. TWO ZERO ROOTS III 466
13.5. SEVERAL PURE IMAGINARY EIGENVALUES 471 13.6. BIBLIOGRAPHICAL NOTES
475 CHAPTER 14 PERTURBATION OF SPECTRA OF LINEAR OPERATORS 476 14.1.
INTRODUCTION 476 14.2. CONTINUITY PROPERTIES OF THE SPECTRUM 477 14.3.
SIMPLE EIGENVALUES 482 -** CONTENTS XV 14.4. MULTIPLE NORMAL EIGENVALUES
490 14.5. SELF-ADJOINT OPERATORS 494 14.6. BIBLIOGRAPHICAL NOTES 498
BIBLIOGRAPHY 501 INDEX 523
|
| any_adam_object | 1 |
| author | Chow, Shui-Nee 1943- Hale, Jack K. 1928-2009 |
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| author_role | aut aut |
| author_sort | Chow, Shui-Nee 1943- |
| author_variant | s n c snc j k h jk jkh |
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| callnumber-subject | QA - Mathematics |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.35 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corr. 2. printing |
| format | Book |
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| id | DE-604.BV011157821 |
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| indexdate | 2024-07-09T18:04:58Z |
| institution | BVB |
| isbn | 3540906649 0387906649 |
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| publishDateSearch | 1996 |
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| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Chow, Shui-Nee 1943- Verfasser (DE-588)1043446311 aut Methods of bifurcation theory Shui-Nee Chow ; Jack K. Hale Corr. 2. printing New York [u.a.] Springer 1996 XV, 525 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 251 Literaturverz. S. 501 - 522 Bifurcation theory Functional differential equations Manifolds (Mathematics) Funktional-Differentialgleichung (DE-588)4155668-9 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Nichtlineare Funktionalanalysis (DE-588)4042093-0 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Verzweigung Mathematik (DE-588)4078889-1 s Nichtlineare Funktionalanalysis (DE-588)4042093-0 s DE-604 Nichtlineare Differentialgleichung (DE-588)4205536-2 s Mannigfaltigkeit (DE-588)4037379-4 s 1\p DE-604 Funktional-Differentialgleichung (DE-588)4155668-9 s 2\p DE-604 Hale, Jack K. 1928-2009 Verfasser (DE-588)172122503 aut Grundlehren der mathematischen Wissenschaften 251 (DE-604)BV000000395 251 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007480313&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chow, Shui-Nee 1943- Hale, Jack K. 1928-2009 Methods of bifurcation theory Grundlehren der mathematischen Wissenschaften Bifurcation theory Functional differential equations Manifolds (Mathematics) Funktional-Differentialgleichung (DE-588)4155668-9 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Differentialgleichung (DE-588)4012249-9 gnd Nichtlineare Funktionalanalysis (DE-588)4042093-0 gnd |
| subject_GND | (DE-588)4155668-9 (DE-588)4078889-1 (DE-588)4037379-4 (DE-588)4205536-2 (DE-588)4012249-9 (DE-588)4042093-0 |
| title | Methods of bifurcation theory |
| title_auth | Methods of bifurcation theory |
| title_exact_search | Methods of bifurcation theory |
| title_full | Methods of bifurcation theory Shui-Nee Chow ; Jack K. Hale |
| title_fullStr | Methods of bifurcation theory Shui-Nee Chow ; Jack K. Hale |
| title_full_unstemmed | Methods of bifurcation theory Shui-Nee Chow ; Jack K. Hale |
| title_short | Methods of bifurcation theory |
| title_sort | methods of bifurcation theory |
| topic | Bifurcation theory Functional differential equations Manifolds (Mathematics) Funktional-Differentialgleichung (DE-588)4155668-9 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Differentialgleichung (DE-588)4012249-9 gnd Nichtlineare Funktionalanalysis (DE-588)4042093-0 gnd |
| topic_facet | Bifurcation theory Functional differential equations Manifolds (Mathematics) Funktional-Differentialgleichung Verzweigung Mathematik Mannigfaltigkeit Nichtlineare Differentialgleichung Differentialgleichung Nichtlineare Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007480313&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT chowshuinee methodsofbifurcationtheory AT halejackk methodsofbifurcationtheory |