Lectures on topics in one-parameter bifurcation problems: lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1985
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| Series: | Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research lectures on mathematics and physics / Mathematics
76. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | III, 285 S. graph. Darst. |
| ISBN: | 3540139079 0387139079 |
Staff View
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| 245 | 1 | 0 | |a Lectures on topics in one-parameter bifurcation problems |b lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics |c by P. Rabier |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1985 | |
| 300 | |a III, 285 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | CONTENTS
CHAPTER I. INTRODUCTION TO ONE PARAMETER BIFURCATION PROBLEMS
§ 1. Introduction 1
§ 2. The Lyapunov Schmidt reduction .. 13
§ 3. Introduction to the mathematical method of resolution
(Implicit function theorem and Morse lemma) .. 19
CHAPTER II. A GENERALIZATION OF THE MORSE LEMMA
§ 1. A nondegeneracy condition for homogeneous polynomial
mappings ..36
§ 2. Practical verification of the condition (F N.D.) .. 41
§ 3. A generalization of the Morse lemma for mappings from
Fn+1 into ]Rn : weak regularity results .. 50
§ 4. Further regularity results .. 60
§ 5. A generalization of the strong version of the Morse
lemma .. 68
CHAPTER III. APPLICATION TO SOME NONDEGENERATE PROBLEMS
§ 1. Equivalence of two Lyapunov Schmidt reductions .. 73
§ 2. Application to problems of bifurcation from the trivial
branch at a multiple characteristic value .. 82
§ 3. Application to a problem with no branch of solutions
known a priori .. 109
CHAPTER IV. AN ALGORITHM FOR THE COMPUTATION OF THE BRANCHES
§ 1. A short review of the method of Chapter II .. 128
§ 2. Equivalence of each equation with a fixed point problem .. 129
§ 3. Convergence of the successive approximation method .. 136
§ 4. Description of the algorithm .. 139
§ 5. A generalization to the case when the mapping f is
not explicitly known .. 142
§ 6. Application to one parameter problems .. 149
CHAPTER V. INTRODUCTION TO A DESINGULARIZATION PROCESS IN THE
STUDY OF DEGENERATE CASES
§ 1. Formulation of the problem and preliminaries .. 164
§ 2. Desingularization by blowing up procedure .. 168
§ 3. Solution through the Implicit function theorem :
cusp bifurcation .. 174
§ 4. Solution through the Morse lemma : isolated solution
and double limit bifurcation .. 179
§ 5. Iteration of the process .. 188
§ 6. Partial results on the intrinsic character of the
process .. 199
§ 7. An analytic proof of Krasnoselskii s theorem in a
non classical particular case .. 207
§ 8. The case of an infinite process .. 219
§ 9. Concluding remarks on further possible developments .. 232
APPENDIX 1 : Practical verification of the conditions (K N.D.) and
(C N.D.) when n = 2 and remarks on the general case .. 237
APPENDIX 2 : Complements to Chapter IV .. 247
REFERENCES .. 282
|
| any_adam_object | 1 |
| author | Rabier, Patrick |
| author_facet | Rabier, Patrick |
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| building | Verbundindex |
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| classification_rvk | SI 890 |
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| ctrlnum | (OCoLC)630506825 (DE-599)BVBBV002119096 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002119096 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:39Z |
| institution | BVB |
| isbn | 3540139079 0387139079 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001389600 |
| oclc_num | 630506825 |
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| physical | III, 285 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer |
| record_format | marc |
| series2 | Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research lectures on mathematics and physics / Mathematics |
| spelling | Rabier, Patrick Verfasser aut Lectures on topics in one-parameter bifurcation problems lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics by P. Rabier Berlin u.a. Springer 1985 III, 285 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research lectures on mathematics and physics / Mathematics 76. Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s DE-604 Mathematics Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research lectures on mathematics and physics 76. (DE-604)BV000015654 76 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001389600&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rabier, Patrick Lectures on topics in one-parameter bifurcation problems lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics Verzweigung Mathematik (DE-588)4078889-1 gnd |
| subject_GND | (DE-588)4078889-1 |
| title | Lectures on topics in one-parameter bifurcation problems lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics |
| title_auth | Lectures on topics in one-parameter bifurcation problems lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics |
| title_exact_search | Lectures on topics in one-parameter bifurcation problems lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics |
| title_full | Lectures on topics in one-parameter bifurcation problems lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics by P. Rabier |
| title_fullStr | Lectures on topics in one-parameter bifurcation problems lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics by P. Rabier |
| title_full_unstemmed | Lectures on topics in one-parameter bifurcation problems lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics by P. Rabier |
| title_short | Lectures on topics in one-parameter bifurcation problems |
| title_sort | lectures on topics in one parameter bifurcation problems lectures delivered at the indian inst of science bangalore under the t i f r i i sc programme in applications of mathematics |
| title_sub | lectures delivered at the Indian Inst. of Science, Bangalore under the T. I. F. R.-I. I. Sc. programme in applications of mathematics |
| topic | Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Verzweigung Mathematik |
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| volume_link | (DE-604)BV000015654 |
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