Geometrical methods in the theory of ordinary differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
1988
|
| Edition: | 2. ed. |
| Series: | Die Grundlehren der mathematischen Wissenschaften
250 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 351 S. graph. Darst. |
| ISBN: | 0387966498 3540966498 9781461269946 |
Staff View
MARC
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| 245 | 1 | 0 | |a Geometrical methods in the theory of ordinary differential equations |c V. I. Arnold |
| 250 | |a 2. ed. | ||
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Record in the Search Index
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| adam_text | Contents
Preface to the Second Edition v
Preface to the First Edition vii
Notation xiii
Chapter 1
Special Equations 1
§ 1. Differential Equations Invariant under Groups of Symmetries 1
§ 2. Resolution of Singularities of Differential Equations 9
§ 3. Implicit Equations 14
§ 4. Normal Form of an Implicit Differential Equation in the Neighborhood of
a Regular Singular Point 25
§ 5. The Stationary Schrodinger Equation 31
§ 6. Geometry of a Second Order Differential Equation and Geometry of a
Pair of Direction Fields in Three Dimensional Space 43
Chapter 2
First Order Partial Differential Equations 59
§ 7. Linear and Quasilinear First Order Partial Differential Equations 59
§ 8. The Nonlinear First Order Partial Differential Equation 68
§ 9. A Theorem of Frobenius 86
Chapter 3
Structural Stability 89
§ 10. The Notion of Structural Stability 89
§11. Differential Equations on the Torus 97
§ 12. Analytic Reduction of Analytic Circle Diffeomorphisms to a Rotation.. 114
§ 13. Introduction to the Hyperbolic Theory 121
§ 14. Anosov Systems 128
§ 15. Structurally Stable Systems Are Not Everywhere Dense 141
Chapter 4
Perturbation Theory 144
§ 16. The Averaging Method 144
§ 17. Averaging in Single Frequency Systems 148
ij 18. Averaging in Systems with Several Frequencies 153
xii Contents
§ 19. Averaging in Hamiltonian Systems 164
§ 20. Adiabatic Invariants 168
§ 21. Averaging in Seifert s Foliation 173
Chapter 5
Normal Forms 180
§ 22. Formal Reduction to Linear Normal Forms 180
§ 23. The Case of Resonance 184
§ 24. Poincare and Siegel Domains 187
§ 25. Normal Form of a Mapping in the Neighborhood of a Fixed Point 192
§ 26. Normal Form of an Equation with Periodic Coefficients 195
§ 27. Normal Form of the Neighborhood of an Elliptic Curve 202
§ 28. Proof of Siegel s Theorem 214
Chapter 6
Local Bifurcation Theory 222
§ 29. Families and Deformations 222
§ 30. Matrices Depending on Parameters and Singularities of the Decrement
Diagram 238
§ 31. Bifurcations of Singular Points of a Vector Field 260
§ 32. Versal Deformations of Phase Portraits 265
§ 33. Loss of Stability of an Equilibrium Position 270
§ 34. Loss of Stability of Self Sustained Oscillations 286
§ 35. Versal Deformations of Equivariant Vector Fields on the Plane 302
§ 36. Metamorphoses of the Topology at Resonances 323
§ 37. Classification of Singular Points 337
Samples of Examination Problems 342
Index 345
|
| any_adam_object | 1 |
| author | Arnolʹd, V. I. 1937-2010 |
| author_GND | (DE-588)119540878 |
| author_facet | Arnolʹd, V. I. 1937-2010 |
| author_role | aut |
| author_sort | Arnolʹd, V. I. 1937-2010 |
| author_variant | v i a vi via |
| building | Verbundindex |
| bvnumber | BV002248703 |
| callnumber-first | Q - Science |
| callnumber-label | QA372 |
| callnumber-raw | QA372 |
| callnumber-search | QA372 |
| callnumber-sort | QA 3372 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 500 SK 520 |
| classification_tum | MAT 146f MAT 349f MAT 145f MAT 587f MAT 340f |
| ctrlnum | (OCoLC)263102747 (DE-599)BVBBV002248703 |
| dewey-full | 515.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/5 |
| dewey-search | 515.3/5 |
| dewey-sort | 3515.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV002248703 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T07:06:26Z |
| institution | BVB |
| isbn | 0387966498 3540966498 9781461269946 |
| language | English |
| lccn | 87027502 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001477668 |
| oclc_num | 263102747 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-739 DE-824 DE-862 DE-BY-FWS DE-355 DE-BY-UBR DE-29T DE-92 DE-703 DE-706 DE-634 DE-83 DE-11 DE-188 DE-384 |
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| physical | XII, 351 S. graph. Darst. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| series | Die Grundlehren der mathematischen Wissenschaften |
| series2 | Die Grundlehren der mathematischen Wissenschaften |
| spellingShingle | Arnolʹd, V. I. 1937-2010 Geometrical methods in the theory of ordinary differential equations Die Grundlehren der mathematischen Wissenschaften Differential equations Differentialgleichung (DE-588)4012249-9 gnd Singularität Mathematik (DE-588)4077459-4 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Geometrie (DE-588)4020236-7 gnd Geometrische Methode (DE-588)4156715-8 gnd Theorie (DE-588)4059787-8 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4077459-4 (DE-588)4020929-5 (DE-588)4020236-7 (DE-588)4156715-8 (DE-588)4059787-8 |
| title | Geometrical methods in the theory of ordinary differential equations |
| title_alt | Dopolnitel'nye glavy teorii obyknovennych differencial'nych uravnenii |
| title_auth | Geometrical methods in the theory of ordinary differential equations |
| title_exact_search | Geometrical methods in the theory of ordinary differential equations |
| title_full | Geometrical methods in the theory of ordinary differential equations V. I. Arnold |
| title_fullStr | Geometrical methods in the theory of ordinary differential equations V. I. Arnold |
| title_full_unstemmed | Geometrical methods in the theory of ordinary differential equations V. I. Arnold |
| title_short | Geometrical methods in the theory of ordinary differential equations |
| title_sort | geometrical methods in the theory of ordinary differential equations |
| topic | Differential equations Differentialgleichung (DE-588)4012249-9 gnd Singularität Mathematik (DE-588)4077459-4 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Geometrie (DE-588)4020236-7 gnd Geometrische Methode (DE-588)4156715-8 gnd Theorie (DE-588)4059787-8 gnd |
| topic_facet | Differential equations Differentialgleichung Singularität Mathematik Gewöhnliche Differentialgleichung Geometrie Geometrische Methode Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001477668&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT arnolʹdvi dopolnitelnyeglavyteoriiobyknovennychdifferencialnychuravnenii AT arnolʹdvi geometricalmethodsinthetheoryofordinarydifferentialequations |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 520 A759 G3(2) |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |