Differential equations and dynamical systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2007
|
| Edition: | 3. ed. ( corr. as of the 5. print.) |
| Series: | Texts in applied mathematics
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 561 S. graph. Darst. |
| ISBN: | 9780387951164 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804137758479876096 |
|---|---|
| adam_text | Contents
Series
Preface
vii
Preface
ix
Linear Systems
1
1.1
Uncoupled
Linear Systems
1
1.2
Diagonalization
6
1.3
Exponentials of Operators
10
1.4
The Fundamental
Theorem for
Linear Systems
16
1.5
Linear Systems in R2
19
1.6
Complex
Eigenvalues
27
1.7
Multiple
Eigenvalues
31
1.8
Jordan Forms
38
1.9
Stability Theory
50
1.10
Nonhomogeneous Linear Systems
58
2
Nonlinear Systems: Local Theory
63
2.1
Some Preliminary Concepts and Definitions
63
2.2
The Fundamental Existence-Uniqueness Theorem
68
2.3
Dependence on Initial Conditions and Parameters
77
2.4
The Maximal Interval of Existence
84
2.5
The Flow Defined by a Differential Equation
92
2.6
Linearization
98
2.7
The Stable Manifold Theorem
102
2.8
The Hartman-Grobman Theorem
116
2.9
Stability and Liapunov Functions
125
2.10
Saddles, Nodes, Foci and Centers
133
2.11
Nonhyperbolic Critical Points in R2
142
2.12
Center Manifold Theory
149
2.13
Normal Form Theory
159
2.14
Gradient and Hamiltonian Systems
166
xiv Contents
3
Nonlinear Systems: Global Theory
177
3.1
Dynamical Systems and Global Existence Theorems
178
3.2
Limit Sets and Attractors
187
3.3
Periodic Orbits, Limit Cycles and Separatrix Cycles
197
3.4
The
Poincaré Map
206
3.5
The Stable Manifold Theorem for Periodic Orbits
215
3.6
Hamiltonian Systems with Two-Degrees of Freedom
228
3.7
The
Poincaré-Bendixson
Theory in R2
238
3.8
Lienard Systems
247
3.9
Bendixson s Criteria
258
3.10
The
Poincaré
Sphere and the Behavior at Infinity
261
3.11
Global Phase Portraits and Separatrix Configurations
285
3.12
Index Theory
291
4
Nonlinear Systems: Bifurcation Theory
309
4.1
Structural Stability and Peixoto s Theorem
310
4.2
Bifurcations at Nonhyperbolic Equilibrium Points
328
4.3
Higher Codimension Bifurcations at Nonhyperbolic
Equilibrium Points
336
4.4 Hopf
Bifurcations and Bifurcations of Limit Cycles
from a Multiple Focus
343
4.5
Bifurcations at Nonhyperbolic Periodic Orbits
355
4.6
One-Parameter Families of Rotated Vector Fields
376
4.7
The Global Behavior of One-Parameter Families
of Periodic Orbits
388
4.8
Homoclinic Bifurcations
393
4.9
Melnikov s Method
407
4.10
Global Bifurcations of Systems in R2
423
4.11
Second and Higher Order Melnikov Theory
443
4.12
Franchise s Algorithm for Higher Order Melnikov
Functions
457
4.13
The Takens-Bogdanov Bifurcation
469
4.14
Coppeľs
Problem for Bounded Quadratic Systems
479
4.15
Finite Codimension Bifurcations in the Class
of Bounded Quadratic Systems
518
Appendix
534
References
547
Additional References
549
Index
555
|
| adam_txt |
Contents
Series
Preface
vii
Preface
ix
Linear Systems
1
1.1
Uncoupled
Linear Systems
1
1.2
Diagonalization
6
1.3
Exponentials of Operators
10
1.4
The Fundamental
Theorem for
Linear Systems
16
1.5
Linear Systems in R2
19
1.6
Complex
Eigenvalues
27
1.7
Multiple
Eigenvalues
31
1.8
Jordan Forms
38
1.9
Stability Theory
50
1.10
Nonhomogeneous Linear Systems
58
2
Nonlinear Systems: Local Theory
63
2.1
Some Preliminary Concepts and Definitions
63
2.2
The Fundamental Existence-Uniqueness Theorem
68
2.3
Dependence on Initial Conditions and Parameters
77
2.4
The Maximal Interval of Existence
84
2.5
The Flow Defined by a Differential Equation
92
2.6
Linearization
98
2.7
The Stable Manifold Theorem
102
2.8
The Hartman-Grobman Theorem
116
2.9
Stability and Liapunov Functions
125
2.10
Saddles, Nodes, Foci and Centers
133
2.11
Nonhyperbolic Critical Points in R2
142
2.12
Center Manifold Theory
149
2.13
Normal Form Theory
159
2.14
Gradient and Hamiltonian Systems
166
xiv Contents
3
Nonlinear Systems: Global Theory
177
3.1
Dynamical Systems and Global Existence Theorems
178
3.2
Limit Sets and Attractors
187
3.3
Periodic Orbits, Limit Cycles and Separatrix Cycles
197
3.4
The
Poincaré Map
206
3.5
The Stable Manifold Theorem for Periodic Orbits
215
3.6
Hamiltonian Systems with Two-Degrees of Freedom
228
3.7
The
Poincaré-Bendixson
Theory in R2
238
3.8
Lienard Systems
247
3.9
Bendixson's Criteria
258
3.10
The
Poincaré
Sphere and the Behavior at Infinity
261
3.11
Global Phase Portraits and Separatrix Configurations
285
3.12
Index Theory
291
4
Nonlinear Systems: Bifurcation Theory
309
4.1
Structural Stability and Peixoto's Theorem
310
4.2
Bifurcations at Nonhyperbolic Equilibrium Points
328
4.3
Higher Codimension Bifurcations at Nonhyperbolic
Equilibrium Points
336
4.4 Hopf
Bifurcations and Bifurcations of Limit Cycles
from a Multiple Focus
343
4.5
Bifurcations at Nonhyperbolic Periodic Orbits
355
4.6
One-Parameter Families of Rotated Vector Fields
376
4.7
The Global Behavior of One-Parameter Families
of Periodic Orbits
388
4.8
Homoclinic Bifurcations
393
4.9
Melnikov's Method
407
4.10
Global Bifurcations of Systems in R2
423
4.11
Second and Higher Order Melnikov Theory
443
4.12
Franchise's Algorithm for Higher Order Melnikov
Functions
457
4.13
The Takens-Bogdanov Bifurcation
469
4.14
Coppeľs
Problem for Bounded Quadratic Systems
479
4.15
Finite Codimension Bifurcations in the Class
of Bounded Quadratic Systems
518
Appendix
534
References
547
Additional References
549
Index
555 |
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| edition | 3. ed. ( corr. as of the 5. print.) |
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| genre | 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV023384307 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:17:35Z |
| indexdate | 2024-07-09T21:17:23Z |
| institution | BVB |
| isbn | 9780387951164 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016567358 |
| oclc_num | 228427571 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XIV, 561 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Perko, Lawrence Verfasser aut Differential equations and dynamical systems Lawrence Perko 3. ed. ( corr. as of the 5. print.) New York [u.a.] Springer 2007 XIV, 561 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 7 Differentiable dynamical systems Differential equations, Nonlinear Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s DE-604 Dynamisches System (DE-588)4013396-5 s 2\p DE-604 Differentialgleichung (DE-588)4012249-9 s 3\p DE-604 System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 s 4\p DE-604 Texts in applied mathematics 7 (DE-604)BV002476038 7 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016567358&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Perko, Lawrence Differential equations and dynamical systems Texts in applied mathematics Differentiable dynamical systems Differential equations, Nonlinear Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Dynamisches System (DE-588)4013396-5 gnd System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4205536-2 (DE-588)4013396-5 (DE-588)4116671-1 (DE-588)4012249-9 (DE-588)4020929-5 (DE-588)4143389-0 |
| title | Differential equations and dynamical systems |
| title_auth | Differential equations and dynamical systems |
| title_exact_search | Differential equations and dynamical systems |
| title_exact_search_txtP | Differential equations and dynamical systems |
| title_full | Differential equations and dynamical systems Lawrence Perko |
| title_fullStr | Differential equations and dynamical systems Lawrence Perko |
| title_full_unstemmed | Differential equations and dynamical systems Lawrence Perko |
| title_short | Differential equations and dynamical systems |
| title_sort | differential equations and dynamical systems |
| topic | Differentiable dynamical systems Differential equations, Nonlinear Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Dynamisches System (DE-588)4013396-5 gnd System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differentiable dynamical systems Differential equations, Nonlinear Nichtlineare Differentialgleichung Dynamisches System System von gewöhnlichen Differentialgleichungen Differentialgleichung Gewöhnliche Differentialgleichung Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016567358&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT perkolawrence differentialequationsanddynamicalsystems |