Geometrical methods in the theory of ordinary differential equations:
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York, NY [u.a.]
Springer
1988
|
Ausgabe: | 2. ed. |
Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften
250 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
Beschreibung: | XII, 351 S. graph. Darst. |
ISBN: | 0387966498 3540966498 9781461269946 |
Internformat
MARC
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100 | 1 | |a Arnolʹd, V. I. |d 1937-2010 |e Verfasser |0 (DE-588)119540878 |4 aut | |
240 | 1 | 0 | |a Dopolnitel'nye glavy teorii obyknovennych differencial'nych uravnenii |
245 | 1 | 0 | |a Geometrical methods in the theory of ordinary differential equations |c V. I. Arnold |
250 | |a 2. ed. | ||
264 | 1 | |a New York, NY [u.a.] |b Springer |c 1988 | |
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Datensatz im Suchindex
DE-BY-862_location | 2000 |
---|---|
DE-BY-FWS_call_number | 2000/SK 520 A759 G3(2) |
DE-BY-FWS_katkey | 53502 |
DE-BY-FWS_media_number | 083000077408 |
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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 | 2024-08-01T16:28:13Z |
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 |
owner_facet | 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 |
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 |
Inhaltsverzeichnis
THWS Schweinfurt Zentralbibliothek Lesesaal
Signatur: |
2000 SK 520 A759 G3(2) |
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Exemplar 1 | ausleihbar Verfügbar Bestellen |