Ordinary differential equations and dynamical systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
2012
|
| Schriftenreihe: | Graduate studies in mathematics
140 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 356 S. |
| ISBN: | 9780821883280 |
Internformat
MARC
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| 100 | 1 | |a Teschl, Gerald |d 1970- |e Verfasser |0 (DE-588)140501037 |4 aut | |
| 245 | 1 | 0 | |a Ordinary differential equations and dynamical systems |c Gerald Teschl |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2012 | |
| 300 | |a XI, 356 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 140 | |
| 650 | 4 | |a Differential equations |v Textbooks | |
| 650 | 4 | |a Dynamics |v Textbooks | |
| 650 | 7 | |a Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.) |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory -- Instructional exposition (textbooks, tutorial papers, etc.) |2 msc | |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |D s |
| 689 | 0 | 1 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-8218-9104-9 |
| 830 | 0 | |a Graduate studies in mathematics |v 140 |w (DE-604)BV009739289 |9 140 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025280214&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025280214 | ||
Datensatz im Suchindex
| _version_ | 1804149489098817536 |
|---|---|
| adam_text | Contents
Preface
ix
Part
1.
Classical theory
Chapter
1.
Introduction
3
§1.1.
Newton s equations
3
§1.2.
Classification of differential equations
б
§1.3.
First-order autonomous equations
9
§1.4.
Finding explicit solutions
13
§1.5.
Qualitative analysis of first-order equations
20
§1.6.
Qualitative analysis of first-order periodic equations
28
Chapter
2.
Initial value problems
33
§2.1.
Fixed point theorems
33
§2.2.
The basic existence and uniqueness result
36
§2.3.
Some extensions
39
§2.4.
Dependence on the initial condition
42
§2.5.
Regular perturbation theory
48
§2.6.
Extensibility of solutions
50
§2.7.
Euler s method and the Peano theorem
54
Chapter
3.
Linear equations
59
§3.1.
The matrix exponential
59
§3.2.
Linear autonomous first-order systems
66
§3.3.
Linear autonomous equations of order
η
74
vi
Contents
§3.4.
General linear
first-order systems
80
§3.5.
Linear
equations of order
η
87
§3.6.
Periodic linear systems
91
§3.7.
Perturbed linear first-order systems
97
§3.8.
Appendix: Jordan canonical form
103
Chapter
4.
Differential equations in the complex domain 111
§4.1.
The basic existence and uniqueness result 111
§4.2.
The Frobenius method for second-order equations
116
§4.3.
Linear systems with singularities
130
§4.4.
The Frobenius method
134
Chapter
5.
Boundary value problems
141
§5.1.
Introduction
141
§5.2.
Compact symmetric operators
146
§5.3.
Sturm-Liouville equations
153
§5.4.
Regular Sturm-Liouville problems
155
§5.5.
Oscillation theory
166
§5.6.
Periodic Sturm-Liouville equations
175
Part
2.
Dynamical systems
Chapter
6.
Dynamical systems
187
§6.1.
Dynamical systems
187
§6.2.
The flow of an autonomous equation
188
§6.3.
Orbits and invariant sets
192
§6.4.
The
Poincaré
map
197
§6.5.
Stability of fixed points
198
§6.6.
Stability via Liapunov s method
201
§6.7.
Newton s equation in one dimension
203
Chapter
7.
Planar dynamical systems
209
§7.1.
Examples from ecology
209
§7.2.
Examples from electrical engineering
215
§7.3.
The
Poincaré-Bendixson
theorem
220
Chapter
8.
Higher dimensional dynamical systems
229
§8.1.
Attracting sets
229
§8.2.
The
Lorenz
equation
234
Contents
vii
§8.3. Hamiltonian
mechanics
238
§8.4.
Completely
integrable
Hamiltonian systems
243
§8.5.
The Kepler problem
247
§8.6.
The
KAM
theorem
250
Chapter
9.
Local behavior near fixed points
255
§9.1.
Stability of linear systems
255
§9.2.
Stable and unstable manifolds
257
§9.3.
The Hartman-Grobman theorem
264
§9.4.
Appendix: Integral equations
270
Part
3.
Chaos
Chapter
10.
Discrete dynamical systems
281
§10.1.
The logistic equation
281
§10.2.
Fixed and periodic points
284
§10.3.
Linear difference equations
287
§10.4.
Local behavior near fixed points
288
Chapter
11.
Discrete dynamical systems in one dimension
293
§11.1.
Period doubling
293
§11.2.
Sarkovskii s theorem
296
§11.3.
On the definition of chaos
297
§11.4.
Cantor sets and the tent map
300
§11.5.
Symbolic dynamics
303
§11.6.
Strange attractors/repellers and fractal sets
309
§11.7.
Homoclinic orbits as source for chaos
313
Chapter
12.
Periodic solutions
317
§12.1.
Stability of periodic solutions
317
§12.2.
The
Poincaré
map
319
§12.3.
Stable and unstable manifolds
321
§12.4.
Melnikov s method for autonomous perturbations
324
§12.5.
Melnikov s method for nonautonomous perturbations
329
Chapter
13.
Chaos in higher dimensional systems
333
§13.1.
The
Smale
horseshoe
333
§13.2.
The Smale-Birkhoff homoclinic theorem
335
§13.3.
Melnikov s method for homoclinic orbits
336
viii Contents
Bibliographical notes
341
Bibliography
345
Glossary of notation
349
Index
351
|
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| dewey-full | 515/.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040427654 |
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| indexdate | 2024-07-10T00:23:50Z |
| institution | BVB |
| isbn | 9780821883280 |
| language | English |
| lccn | 2012015024 |
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| series | Graduate studies in mathematics |
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| spelling | Teschl, Gerald 1970- Verfasser (DE-588)140501037 aut Ordinary differential equations and dynamical systems Gerald Teschl Providence, R.I. American Mathematical Society 2012 XI, 356 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 140 Differential equations Textbooks Dynamics Textbooks Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.) msc Dynamical systems and ergodic theory -- Instructional exposition (textbooks, tutorial papers, etc.) msc Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Dynamisches System (DE-588)4013396-5 s DE-604 Erscheint auch als Online-Ausgabe 978-0-8218-9104-9 Graduate studies in mathematics 140 (DE-604)BV009739289 140 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025280214&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Teschl, Gerald 1970- Ordinary differential equations and dynamical systems Graduate studies in mathematics Differential equations Textbooks Dynamics Textbooks Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.) msc Dynamical systems and ergodic theory -- Instructional exposition (textbooks, tutorial papers, etc.) msc Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4013396-5 |
| title | Ordinary differential equations and dynamical systems |
| title_auth | Ordinary differential equations and dynamical systems |
| title_exact_search | Ordinary differential equations and dynamical systems |
| title_full | Ordinary differential equations and dynamical systems Gerald Teschl |
| title_fullStr | Ordinary differential equations and dynamical systems Gerald Teschl |
| title_full_unstemmed | Ordinary differential equations and dynamical systems Gerald Teschl |
| title_short | Ordinary differential equations and dynamical systems |
| title_sort | ordinary differential equations and dynamical systems |
| topic | Differential equations Textbooks Dynamics Textbooks Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.) msc Dynamical systems and ergodic theory -- Instructional exposition (textbooks, tutorial papers, etc.) msc Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Differential equations Textbooks Dynamics Textbooks Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.) Dynamical systems and ergodic theory -- Instructional exposition (textbooks, tutorial papers, etc.) Gewöhnliche Differentialgleichung Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025280214&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
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