Point mapping stability:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Pergamon Pr.
1977
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 103 S. Ill. u. graph. Darst. |
| ISBN: | 0080212832 |
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MARC
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| 100 | 1 | |a Bernussou, Jacques |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Point mapping stability |
| 264 | 1 | |a Oxford |b Pergamon Pr. |c 1977 | |
| 300 | |a XI, 103 S. |b Ill. u. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Applications (Mathématiques) | |
| 650 | 4 | |a Stabilité | |
| 650 | 4 | |a Transformations, Groupes de | |
| 650 | 4 | |a Équations différentielles | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Functional differential equations |x Numerical solutions | |
| 650 | 4 | |a Point mappings (Mathematics) | |
| 650 | 4 | |a Stability | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Foreword by j. lagasse vii
Preface by wolfgang hahn ix
Acknowledgements xi
Chapter I Fundamentals on point mappings l
1.1. Some of the main motivations for studying point mappings 1
1.2. Some definitions 2
1.2.1. Characteristic equation. Multipliers. Stability 3
1.2.2. Classification of the singularities 3
1.2.3. Analytic invariant curves 5
1.2.4. Other definitions 6
1.2.4.1. Singularities at infinity 6
1.2.4.2. Critical curves 6
1.2.4.3. Poincare index b
1.3. Some of the main problems involved in studying point mappings 7
Chapter II Critical cases 9
11.1. Introduction 9
11.2. Critical case with one multiplier equal to one 9
II. 2.1. First order point mapping 9
II.2.2. General case. Some remarks 10
11.3. Generalities. Malkin s contribution 12
II .3.1. Notion of stability according to the m degree approximation 12
II.3.2. Dimensionality reduction 13
II.U. Critical cases with two multipliers of absolute value unity 13
II .4.1. Complex multipliers 13
II.4. 1.1. Second order point mapping 13
II.4.1.2. General case 15
11.4.2. Real multipliers. Linear diagonal part 16
11.4.2.1. Assumptions. Preliminary transformations 16
11.4.2.2. Qm(w)jto, we[0,2tt] 17
11.4.2.3. Qm(w) of sign not defined 17
11.4.2.4. Summary 21
11.4.3. Non diagonal linear part 21
11.4.3.1. Preliminary transformations. Normal forms 21
11.4.3.2. Invariant curves 22
11.4.3.3. Other cases 23
11.5. Some cases where the number of critical multipliers is higher
than 2 26
11.6. Conclusion 29
3C
Appendix I Calculation of G^
Appendix 2
v£ Contents
Chapter III Differential systems with periodic coefficients 35
111.1. Point mapping and the associated formal differential system 35
III. 1.1 . Generalities 35
III. 1.2. Determination of the series x ,y 37
III.1.3. Formal differential system 38
111.2. Determination of the mapping associated with a non linear
differential equation with periodic coefficients 38
111.2.1. Brief description of the method 38
111.2.2. Some calculations 39
111.3. Other forms of differential equations 40
111.3.1. Mapping with complex multipliers 41
111.3.2. Mapping with real multipliers 41
Appendix 44
Chapter IV Parametric resonance. Conservative systems 47
IV.1. Parametric resonance 47
IV.1.1. The exceptional cases w = 2kir/q 47
IV.1.2. q=2 48
IV.1.3. q=3 48
IV. 1.4. q=4 51
IV.1.5. Generalisation 53
IV.1.6. Example 54
IV.2. Conservative systems 56
IV.2.1. Area preserving point mapping. Specific problems 57
IV.2.2. The numerical studies 59
IV.2.3. Periodic hamiltonian systems 60
IV.2.4. Preliminary remarks 61
IV.2.5. Approximating mapping. Osculation up to the second degree
terms 62
IV.2.6. Approximating mapping. Osculation up to the third degree
terms 63
IV.2.7. Example 66
IV.3. Conclusion 72
Appendix 73
Chapter V Practical features, numerical tools. Examples 74
V.1. Determination of singularities 74
V. 1 . 1 . Brief description of the proposed method 75
V.1.2. Coarse systems. Some results 76
V.1.3. Practical implementation 78
V.2. Invariant curves 79
V.2.1. Analytic method 81
V.2.2. Numerical method 84
V.3. Bifurcation phenomenon 85
V.3.1 . S = +1 86
V.3.2. S12 = exp(ljw) 89
V.4. Some examples 90
V.4.1. First example 90
V.4.2. Second example 92
References 97
Author Index 101
Subject Index 103
|
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| id | DE-604.BV001975468 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:13Z |
| institution | BVB |
| isbn | 0080212832 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001288474 |
| oclc_num | 3696498 |
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| physical | XI, 103 S. Ill. u. graph. Darst. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | Pergamon Pr. |
| record_format | marc |
| spelling | Bernussou, Jacques Verfasser aut Point mapping stability Oxford Pergamon Pr. 1977 XI, 103 S. Ill. u. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applications (Mathématiques) Stabilité Transformations, Groupes de Équations différentielles Differentiable dynamical systems Functional differential equations Numerical solutions Point mappings (Mathematics) Stability HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001288474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bernussou, Jacques Point mapping stability Applications (Mathématiques) Stabilité Transformations, Groupes de Équations différentielles Differentiable dynamical systems Functional differential equations Numerical solutions Point mappings (Mathematics) Stability |
| title | Point mapping stability |
| title_auth | Point mapping stability |
| title_exact_search | Point mapping stability |
| title_full | Point mapping stability |
| title_fullStr | Point mapping stability |
| title_full_unstemmed | Point mapping stability |
| title_short | Point mapping stability |
| title_sort | point mapping stability |
| topic | Applications (Mathématiques) Stabilité Transformations, Groupes de Équations différentielles Differentiable dynamical systems Functional differential equations Numerical solutions Point mappings (Mathematics) Stability |
| topic_facet | Applications (Mathématiques) Stabilité Transformations, Groupes de Équations différentielles Differentiable dynamical systems Functional differential equations Numerical solutions Point mappings (Mathematics) Stability |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001288474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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