Introduction to modern dynamics: chaos, networks, space and time
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2015
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027572571&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIII, 423 S. graph. Darst. |
| ISBN: | 9780199657032 0199657033 0199657041 9780199657049 |
Internformat
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| 245 | 1 | 0 | |a Introduction to modern dynamics |b chaos, networks, space and time |c David D. Nolte |
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2015 | |
| 300 | |a XIII, 423 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1819306126875820032 |
|---|---|
| adam_text | Titel: Introduction to modern dynamics
Autor: Nolte, David D
Jahr: 2015
Contents
Part 1 Geometric Mechanics
1 Physics and Geometry 3
1.1 Newton and geometry 4
1.2 State space and flows 12
1.3 Coordinate transformations 18
1.4 Non-inertial transformations 26
1.5 Uniformly rotating frames 29
1.6 Rigid-body motion 35
1.7 Summary 44
1.8 Bibliography 42
1.9 Homework exercises 42
2 Hamiltonian Dynamics and Phase Space 51
2.1 Hamilton s principle 52
2.2 Conservation laws 55
2.3 The Hamiltonian function 60
2.4 Central force motion 66
2.5 Phase space 25
2.6 Integrable systems and action-angle variables 85
2.7 Summary 89
2.8 Bibliography 91
2.9 Homework exercises 92
Part 2 Nonlinear Dynamics
3 Nonlinear Dynamics and Chaos 97
3.1 One-variable dynamical systems 99
3.2 Two-variable dynamical systems 100
3.3 Discrete iterative maps 118
3.4 Three-dimensional state space and chaos 121
3.5 Fractals and strange attractors 131
3.6 Hamiltonian chaos 135
3.7 Summary and glossary 143
3.8 Bibliography 144
3.9 Homework exercises 145
4 Coupled Oscillators and Synchronization 149
4.1 Coupled linear oscillators 150
4.2 Simple models of synchronization 157
xii Contents
4.3 External synchronization of an autonomous phase oscillator 165
4.4 External synchronization of a van der Pol oscillator 168
4.5 Mutual synchronization of two autonomous oscillators 171
4.6 Summary 173
4.7 Bibliography 174
4.8 Homework exercises 175
5 Network Dynamics 178
5.1 Network structures 179
5.2 Random network topologies 183
5.3 Diffusion and epidemics on networks 187
5.4 Linear synchronization of identical oscillators 195
5.5 Nonlinear synchronization of coupled phase oscillators on regular graphs 198
5.6 Summary 204
5.7 Bibliography 205
5.8 Homework exercises 206
Part 3 Complex Systems
6 Neurodynamics and Neural Networks 211
6.1 Neuron structure and function 212
6.2 Neuron dynamics 214
6.3 Network nodes: artificial neurons 219
6.4 Neural network architectures 223
6.5 Hopfield neural network 230
6.6 Content-addressable (associative) memory 232
6.7 Summary 237
6.8 Bibliography 240
6.9 Homework exercises 240
7 Evolutionary Dynamics 242
7.1 Population dynamics 243
7.2 Virus infection and immune deficiency 246
7.3 The replicator equation 250
7.4 The quasi-species equation 253
7.5 The replicator-mutator equation 261
7.6 Dynamics of finite numbers (optional) 263
7.7 Summary 265
7.8 Bibliography 267
7.9 Homework exercises 268
8 Economic Dynamics 270
8.1 Micro-and macroeconomics 271
8.2 Supply and demand 272
8.3 Business cycles 275
Contents xiii
8.4 Consumer market competition 280
8.5 Macroeconomics 285
8.6 Stochastic dynamics and stock prices (optional) 292
8.7 Summary 301
8.8 Bibliography 303
8.9 Homework exercises 303
Part 4 Relativity and Space-Time
9 Metric Spaces and Geodesic Motion 307
9.1 Manifolds and metric tensors 308
9.2 Reciprocal spaces in physics 321
9.3 Derivative of a tensor 322
9.4 Geodesic curves in configuration space 328
9.5 Geodesic motion 339
9.6 Summary 344
9.7 Bibliography 347
9.8 Homework exercises 347
10 Relativistic Dynamics 349
10.1 The special theory 350
10.2 Lorentz transformations 352
10.3 Metric structure of Minkowski space 366
10.4 Relativistic dynamics 371
10.5 Linearly accelerating frames (relativistic) 380
10.6 Summary 384
10.7 Bibliography 386
10.8 Homework exercises 386
11 The General Theory of Relativity and Gravitation 388
11.1 Riemann curvature tensor 388
11.2 The Newtonian correspondence 392
11.3 Einstein s field equations 394
11.4 Schwarzschild space-time 398
11.5 Kinematic consequences of gravity 399
11.6 The deflection of light by gravity 401
11.7 Planetary orbits 405
11.8 Orbits near a black hole 409
11.9 Summary 412
11.10 Bibliography 414
11.11 Homework exercises 415
Index 417
|
| any_adam_object | 1 |
| author | Nolte, David D. 1959- |
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| dewey-full | 531.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
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| discipline | Physik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-12-20T17:03:04Z |
| institution | BVB |
| isbn | 9780199657032 0199657033 0199657041 9780199657049 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027572571 |
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| physical | XIII, 423 S. graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spellingShingle | Nolte, David D. 1959- Introduction to modern dynamics chaos, networks, space and time Dynamics Komplexes System (DE-588)4114261-5 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd Dynamik (DE-588)4013384-9 gnd Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4114261-5 (DE-588)4126141-0 (DE-588)4013384-9 (DE-588)4009754-7 |
| title | Introduction to modern dynamics chaos, networks, space and time |
| title_auth | Introduction to modern dynamics chaos, networks, space and time |
| title_exact_search | Introduction to modern dynamics chaos, networks, space and time |
| title_full | Introduction to modern dynamics chaos, networks, space and time David D. Nolte |
| title_fullStr | Introduction to modern dynamics chaos, networks, space and time David D. Nolte |
| title_full_unstemmed | Introduction to modern dynamics chaos, networks, space and time David D. Nolte |
| title_short | Introduction to modern dynamics |
| title_sort | introduction to modern dynamics chaos networks space and time |
| title_sub | chaos, networks, space and time |
| topic | Dynamics Komplexes System (DE-588)4114261-5 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd Dynamik (DE-588)4013384-9 gnd Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | Dynamics Komplexes System Nichtlineare Dynamik Dynamik Chaostheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027572571&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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