An introduction to dynamical systems: continuous and discrete
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2012
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Pure and applied undergraduate texts
19 |
| Schlagworte: |
Dynamical systems and ergodic theory
> Smooth dynamical systems: general theory
> Smooth dynamical systems: general theory
Dynamical systems and ergodic theory
> Dynamical systems with hyperbolic behavior
> Dynamical systems with hyperbolic behavior
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 733 S. graph. Darst. |
| ISBN: | 9780821891353 |
Internformat
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| 245 | 1 | 0 | |a An introduction to dynamical systems |b continuous and discrete |c R. Clark Robinson |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2012 | |
| 300 | |a XX, 733 S. |b graph. Darst. | ||
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| 490 | 1 | |a Pure and applied undergraduate texts |v 19 | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 7 | |a Ordinary differential equations -- Qualitative theory -- Qualitative theory |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Smooth dynamical systems: general theory |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems with hyperbolic behavior |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory -- Low-dimensional dynamical systems -- Low-dimensional dynamical systems |2 msc | |
| 650 | 7 | |a Dynamical systems and ergodic theory -- Applications -- Applications |2 msc | |
| 650 | 7 | |a Mechanics of particles and systems -- Nonlinear dynamics -- Nonlinear dynamics |2 msc | |
| 650 | 0 | 7 | |a Chaotisches System |0 (DE-588)4316104-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804149782075146240 |
|---|---|
| adam_text | Titel: An introduction to dynamical systems
Autor: Robinson, Rex Clark
Jahr: 2012
Contents
Preface xiii
Historical Prologue xvii
Part 1. Systems of Nonlinear Differential Equations
Chapter 1. Geometrie Approach to Differential Equations 3
Chapter 2. Linear Systems 11
2.1. Fundamental Set of Solutions 13
Exercises 2.1 19
2.2. Constant Coefficients: Solutions and Phase Portraits 21
Exercises 2.2 48
2.3. Nonhomogeneous Systems: Time-dependent Forcing 49
Exercises 2.3 52
2.4. Applications 52
Exercises 2.4 56
2.5. Theory and Proofs 59
Chapter 3. The Flow: Solutions of Nonlinear Equations 75
3.1. Solutions of Nonlinear Equations 75
Exercises 3.1 83
3.2. Numerical Solutions of Differential Equations 84
Exercises 3.2 96
3.3. Theory and Proofs 97
Chapter 4. Phase Portraits with Emphasis on Fixed Points 109
4.1. Limit Sets 109
vii
viii Contents
Exercises 4.1 114
4.2. Stability of Fixed Points 114
Exercises 4.2 119
4.3. Scalar Equations 119
Exercises 4.3 124
4.4. Two Dimensions and Nullclines 126
Exercises 4.4 133
4.5. Linearized Stability of Fixed Points 134
Exercises 4.5 143
4.6. Competitive Populations 145
Exercises 4.6 150
4.7. Applications 152
Exercises 4.7 158
4.8. Theory and Proofs 159
Chapter 5. Phase Portraits Using Scalar Functions 169
5.1. Predator-Prey Systems 169
Exercises 5.1 172
5.2. Undamped Forces 173
Exercises 5.2 182
5.3. Lyapunov Functions for Damped Systems 183
Exercises 5.3 190
5.4. Bounding Functions 191
Exercises 5.4 195
5.5. Gradient Systems 195
Exercises 5.5 199
5.6. Applications 199
Exercises 5.6 210
5.7. Theory and Proofs 210
Chapter 6. Periodic Orbits 213
6.1. Introduction to Periodic Orbits 214
Exercises 6.1 218
6.2. Poincare-Bendixson Theorem 219
Exercises 6.2 226
6.3. Self-Excited Oscillator 229
Exercises 6.3 232
6.4. Andronov-Hopf Bifurcation 232
Exercises 6.4 240
6.5. Homoclinic Bifurcation 242
Contents ix
Exercises 6.5 246
6.6. Rate of Change of Volume 247
Exercises 6.6 249
6.7. Poincare Map 251
Exercises 6.7 261
6.8. Applications 262
Exercises 6.8 271
6.9. Theory and Proofs 272
Chapter 7. Chaotic Attractors 285
7.1. Attractors 285
Exercises 7.1 289
7.2. Chaotic Attractors 291
Exercise 7.2 296
7.3. Lorenz System 297
Exercises 7.3 312
7.4. Rössler Attractor 313
Exercises 7.4 316
7.5. Forced Oscillator 317
Exercises 7.5 319
7.6. Lyapunov Exponents 320
Exercises 7.6 328
7.7. Test for Chaotic Attractors 329
Exercises 7.7 331
7.8. Applications 331
7.9. Theory and Proofs 336
Part 2. Iteration of Functions
Chapter 8. Iteration of Functions as Dynamics 343
8.1. One-Dimensional Maps 343
8.2. Functions with Several Variables 349
Chapter 9. Periodic Points of One-Dimensional Maps 353
9.1. Periodic Points 353
Exercises 9.1 362
9.2. Iteration Using the Graph 362
Exercises 9.2 366
9.3. Stability of Periodic Points 367
Exercises 9.3 382
9.4. Critical Points and Basins 386
Contents
Exercises 9.4 390
9.5. Bifurcation of Periodic Points 391
Exercises 9.5 404
9.6. Conjugacy 406
Exercises 9.6 411
9.7. Applications 412
Exercises 9.7 416
9.8. Theory and Proofs 417
Chapter 10. Itineraries for One-Dimensional Maps 423
10.1. Periodic Points from Transition Graphs 424
Exercises 10.1 435
10.2. Topological Transitivity 437
Exercises 10.2 441
10.3. Sequences of Symbols 442
Exercises 10.3 451
10.4. Sensitive Dependence on Initial Conditions 451
Exercises 10.4 454
10.5. Cantor Sets 455
Exercises 10.5 463
10.6. Piecewise Expanding Maps and Subshifts 464
Exercises 10.6 473
10.7. Applications 475
Exercises 10.7 478
10.8. Theory and Proofs 479
Chapter 11. Invariant Sets for One-Dimensional Maps 487
11.1. Limit Sets 487
Exercises 11.1 490
11.2. Chaotic Attractors 490
Exercises 11.2 505
11.3. Lyapunov Exponents 507
Exercises 11.3 513
11.4. Invariant Measures 514
Exercises 11.4 533
11.5. Applications 534
11.6. Theory and Proofs 537
Chapter 12. Periodic Points of Higher Dimensional Maps 541
12.1. Dynamics of Linear Maps 541
Contents
XI
Exercises 12.1 555
12.2. Classification of Periodic Points 555
Exercises 12.2 566
12.3. Stable Manifolds 567
Exercises 12.3 575
12.4. Hyperbolic Toral Automorphisms 575
Exercises 12.4 580
12.5. Applications 580
Exercises 12.5 594
12.6. Theory and Proofs 595
Chapter 13. Invariant Sets for Higher Dimensional Maps 597
13.1. Geometrie Horseshoe 598
Exercises 13.1 611
13.2. Symbolic Dynamics 612
Exercises 13.2 632
13.3. Homoclinic Points and Horseshoes 636
Exercises 13.3 639
13.4. Attractors 639
Exercises 13.4 649
13.5. Lyapunov Exponents 650
Exercises 13.5 661
13.6. Applications 662
13.7. Theory and Proofs 664
Chapter 14. Fractals 669
14.1. Box Dimension 670
Exercises 14.1 679
14.2. Dimension of Orbits 680
Exercises 14.2 684
14.3. Iterated-Function Systems 684
Exercises 14.3 696
14.4. Theory and Proofs 697
Appendix A. Background and Terminology 705
A.l. Calculus Background and Notation 705
A.2. Analysis and Topology Terminology 707
A.3. Matrix Algebra 713
Appendix B. Generic Properties 717
721
Bibliography
Index 727
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| isbn | 9780821891353 |
| language | English |
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| spelling | Robinson, Rex Clark 1943- Verfasser (DE-588)130562920 aut An introduction to dynamical systems continuous and discrete R. Clark Robinson 2. ed. Providence, RI American Math. Soc. 2012 XX, 733 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied undergraduate texts 19 Differentiable dynamical systems Nonlinear theories Chaotic behavior in systems Ordinary differential equations -- Qualitative theory -- Qualitative theory msc Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Smooth dynamical systems: general theory msc Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems with hyperbolic behavior msc Dynamical systems and ergodic theory -- Low-dimensional dynamical systems -- Low-dimensional dynamical systems msc Dynamical systems and ergodic theory -- Applications -- Applications msc Mechanics of particles and systems -- Nonlinear dynamics -- Nonlinear dynamics msc Chaotisches System (DE-588)4316104-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Chaotisches System (DE-588)4316104-2 s DE-604 Pure and applied undergraduate texts 19 (DE-604)BV035489189 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025486343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Robinson, Rex Clark 1943- An introduction to dynamical systems continuous and discrete Pure and applied undergraduate texts Differentiable dynamical systems Nonlinear theories Chaotic behavior in systems Ordinary differential equations -- Qualitative theory -- Qualitative theory msc Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Smooth dynamical systems: general theory msc Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems with hyperbolic behavior msc Dynamical systems and ergodic theory -- Low-dimensional dynamical systems -- Low-dimensional dynamical systems msc Dynamical systems and ergodic theory -- Applications -- Applications msc Mechanics of particles and systems -- Nonlinear dynamics -- Nonlinear dynamics msc Chaotisches System (DE-588)4316104-2 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4316104-2 (DE-588)4013396-5 |
| title | An introduction to dynamical systems continuous and discrete |
| title_auth | An introduction to dynamical systems continuous and discrete |
| title_exact_search | An introduction to dynamical systems continuous and discrete |
| title_full | An introduction to dynamical systems continuous and discrete R. Clark Robinson |
| title_fullStr | An introduction to dynamical systems continuous and discrete R. Clark Robinson |
| title_full_unstemmed | An introduction to dynamical systems continuous and discrete R. Clark Robinson |
| title_short | An introduction to dynamical systems |
| title_sort | an introduction to dynamical systems continuous and discrete |
| title_sub | continuous and discrete |
| topic | Differentiable dynamical systems Nonlinear theories Chaotic behavior in systems Ordinary differential equations -- Qualitative theory -- Qualitative theory msc Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Smooth dynamical systems: general theory msc Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems with hyperbolic behavior msc Dynamical systems and ergodic theory -- Low-dimensional dynamical systems -- Low-dimensional dynamical systems msc Dynamical systems and ergodic theory -- Applications -- Applications msc Mechanics of particles and systems -- Nonlinear dynamics -- Nonlinear dynamics msc Chaotisches System (DE-588)4316104-2 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Differentiable dynamical systems Nonlinear theories Chaotic behavior in systems Ordinary differential equations -- Qualitative theory -- Qualitative theory Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Smooth dynamical systems: general theory Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems with hyperbolic behavior Dynamical systems and ergodic theory -- Low-dimensional dynamical systems -- Low-dimensional dynamical systems Dynamical systems and ergodic theory -- Applications -- Applications Mechanics of particles and systems -- Nonlinear dynamics -- Nonlinear dynamics Chaotisches System Dynamisches System |
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