Complex nonlinearity: chaos, phase transitions, topology change and path integrals
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2008
|
| Series: | Understanding complex systems
Springer complexity |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 713 - 830 |
| Physical Description: | XV, 844 S. graph. Darst. 24 cm |
| ISBN: | 9783540793564 |
Staff View
MARC
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| 100 | 1 | |a Ivancevic, Vladimir G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Complex nonlinearity |b chaos, phase transitions, topology change and path integrals |c Vladimir G. Ivancevic ; Tijana T. Ivancevic |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2008 | |
| 300 | |a XV, 844 S. |b graph. Darst. |c 24 cm | ||
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| 490 | 0 | |a Understanding complex systems | |
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| 700 | 1 | |a Ivancevic, Tijana T. |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804148606821728256 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
BASICS OF NONLINEAR AND CHAOTIC DYNAMICS 1
1.1 INTRODUCTION TO CHAOS THEORY 1
1.2 BASICS OF ATTRACTOR AND CHAOTIC DYNAMICS 16
1.3 BRIEF HISTORY OF CHAOS THEORY 25
1.3.1 POINCARE S QUALITATIVE DYNAMICS, TOPOLOGY AND CHAOS . 26 1.3.2
SMALE S TOPOLOGICAL HORSESHOE AND CHAOS OF STRETCHING AND FOLDING 34
1.3.3 LORENZ WEATHER PREDICTION AND CHAOS 44
1.3.4 FEIGENBAUM S CONSTANT AND UNIVERSALITY 47
1.3.5 MAY S POPULATION MODELLING AND CHAOS 48
1.3.6 HENON S SPECIAL 2D MAP AND ITS STRANGE ATTRACTOR . . .. 52 1.4
MORE CHAOTIC AND ATTRACTOR SYSTEMS 55
1.5 CONTINUOUS CHAOTIC DYNAMICS 67
1.5.1 DYNAMICS AND NON-EQUILIBRIUM STATISTICAL MECHANICS.. 69 1.5.2
STATISTICAL MECHANICS OF NONLINEAR OSCILLATOR CHAINS . .. 82 1.5.3
GEOMETRICAL MODELLING OF CONTINUOUS DYNAMICS 84 1.5.4 LAGRANGIAN CHAOS
86
1.6 STANDARD MAP AND HAMILTONIAN CHAOS 95
1.7 CHAOTIC DYNAMICS OF BINARY SYSTEMS 101
1.7.1 EXAMPLES OF DYNAMICAL MAPS 103
1.7.2 CORRELATION DIMENSION OF AN ATTRACTOR 107
1.8 SPATIO-TEMPORAL CHAOS AND TURBULENCE IN PDES 108 1.8.1 TURBULENCE
108
1.8.2 SINE-GORDON EQUATION 113
1.8.3 COMPLEX GINZBURG-LANDAU EQUATION 114
1.8.4 KURAMOTCH-SIVASHINSKY SYSTEM 115
1.8.5 BURGERS DYNAMICAL SYSTEM 116
1.8.6 2D KURAMOTO-SIVASHINSKY EQUATION 118
1.9 BASICS OF CHAOS CONTROL 124
1.9.1 FEEDBACK AND NON-FEEDBACK ALGORITHMS FOR CHAOS CONTROL 124
GESCANNT DURCH
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/988008793
DIGITALISIERT DURCH
IMAGE 2
XII CONTENTS
1.9.2 EXPLOITING CRITICAL SENSITIVITY 127
1.9.3 LYAPUNOV EXPONENTS AND KAPLAN-YORKE DIMENSION.... 129 1.9.4
KOLMOGOROV-SINAI ENTROPY 131
1.9.5 CHAOS CONTROL BY OTT, GREBOGI AND YORKE (OGY) 132 1.9.6 FLOQUET
STABILITY ANALYSIS AND OGY CONTROL 135 1.9.7 BLIND CHAOS CONTROL 139
1.9.8 JERK FUNCTIONS OF SIMPLE CHAOTIC FLOWS 143 1.9.9 EXAMPLE: CHAOS
CONTROL IN MOLECULAR DYNAMICS 146 1.10 SPATIO-TEMPORAL CHAOS CONTROL 155
1.10.1 MODELS OF SPATIO-TEMPORAL CHAOS IN EXCITABLE MEDIA .. 158 1.10.2
GLOBAL CHAOS CONTROL 160
1.10.3 NON-GLOBAL SPATIALLY EXTENDED CONTROL 163 1.10.4 LOCAL CHAOS
CONTROL 165
1.10.5 SPATIO-TEMPORAL CHAOS-CONTROL IN THE HEART 166
2 PHASE TRANSITIONS AND SYNERGETICS 173
2.1 INTRODUCTION TO PHASE TRANSITIONS 173
2.1.1 EQUILIBRIUM PHASE TRANSITIONS 173
2.1.2 CLASSIFICATION OF PHASE TRANSITIONS 175
2.1.3 BASIC PROPERTIES OF PHASE TRANSITIONS 176
2.1.4 LANDAU S THEORY OF PHASE TRANSITIONS 179
2.1.5 EXAMPLE: ORDER PARAMETERS IN MAGNETITE PHASE TRANSITION 180
2.1.6 UNIVERSAL MANDELBROT SET AS A PHASE-TRANSITION MODEL 183 2.1.7
OSCILLATORY PHASE TRANSITION 187
2.1.8 PARTITION FUNCTION AND ITS PATH-INTEGRAL DESCRIPTION. .. 192 2.1.9
NOISE-INDUCED NON-EQUILIBRIUM PHASE TRANSITIONS . . .. 199 2.1.10
NOISE-DRIVEN FERROMAGNETIC PHASE TRANSITION 206 2.1.11 PHASE TRANSITION
IN A REACTION-DIFFUSION SYSTEM 218
2.1.12 PHASE TRANSITION IN NEGOTIATION DYNAMICS 224 2.2 ELEMENTS OF
HAKEN S SYNERGETICS 229
2.2.1 PHASE TRANSITIONS AND SYNERGETICS 231
2.2.2 ORDER PARAMETERS IN HUMAN/HUMANOID BIODYNAMICS . . 233 2.2.3
EXAMPLE: SYNERGETIC CONTROL OF BIODYNAMICS 236 2.2.4 EXAMPLE: CHAOTIC
PSYCHODYNAMICS OF PERCEPTION 237 2.2.5 KICK DYNAMICS AND
DISSIPATION-FLUCTUATION THEOREM.. 241 2.3 SYNERGETICS OF RECURRENT AND
ATTRACTOR NEURAL NETWORKS 244
2.3.1 STOCHASTIC DYNAMICS OF NEURONAL FIRING STATES 246 2.3.2 SYNAPTIC
SYMMETRY AND LYAPUNOV FUNCTIONS 251 2.3.3 DETAILED BALANCE AND
EQUILIBRIUM STATISTICAL MECHANICS 253 2.3.4 SIMPLE RECURRENT NETWORKS
WITH BINARY NEURONS 259
2.3.5 SIMPLE RECURRENT NETWORKS OF COUPLED OSCILLATORS 267 2.3.6
ATTRACTOR NEURAL NETWORKS WITH BINARY NEURONS 275 2.3.7 ATTRACTOR NEURAL
NETWORKS WITH CONTINUOUS NEURONS .. 287 2.3.8 CORRELATION- AND
RESPONSE-FUNCTIONS 293
IMAGE 3
CONTENTS XIII
GEOMETRY AND TOPOLOGY CHANGE IN COMPLEX SYSTEMS 305 3.1 RIEMANNIAN
GEOMETRY OF SMOOTH MANIFOLDS 305
3.1.1 RIEMANNIAN MANIFOLDS: AN INTUITIVE PICTURE 305
3.1.2 SMOOTH MANIFOLDS AND THEIR (CO)TANGENT BUNDLES 317 3.1.3 LOCAL
RIEMANNIAN GEOMETRY 328
3.1.4 GLOBAL RIEMANNIAN GEOMETRY 338
3.2 RIEMANNIAN APPROACH TO CHAOS 343
3.2.1 GEOMETRIZATION OF NEWTONIAN DYNAMICS 345
3.2.2 GEOMETRIE DESCRIPTION OF DYNAMICAL INSTABILITY 347 3.2.3 EXAMPLES
361
3.3 MORSE TOPOLOGY OF SMOOTH MANIFOLDS 368
3.3.1 INTRO TO EULER CHARACTERISTIC AND MORSE TOPOLOGY 368 3.3.2 SETS
AND TOPOLOGICAL SPACES 371
3.3.3 A BRIEF INTRO TO MORSE THEORY 380
3.3.4 MORSE THEORY AND ENERGY FUNCTIONALS 382
3.3.5 MORSE THEORY AND RIEMANNIAN GEOMETRY 384
3.3.6 MORSE TOPOLOGY IN HUMAN/HUMANOID BIODYNAMICS.... 388 3.3.7
COBORDISM TOPOLOGY ON SMOOTH MANIFOLDS 392
3.4 TOPOLOGY CHANGE IN 3D 394
3.4.1 ATTACHING HANDIES 396
3.4.2 ORIENTED COBORDISM AND SURGERY THEORY 402
3.5 TOPOLOGY CHANGE IN QUANTUM GRAVITY 405
3.5.1 A TOP-DOWN FRAMEWORK FOR TOPOLOGY CHANGE 405 3.5.2 MORSE METRICS
AND ELEMENTARY TOPOLOGY CHANGES 406 3.5.3 GOOD AND BAD TOPOLOGY
CHANGE 408
3.5.4 BORDE-SORKIN CONJECTURE 410
3.6 A HANDLE-BODY CALCULUS FOR TOPOLOGY CHANGE 411
3.6.1 HANDLE-BODY DECOMPOSITIONS 414
3.6.2 INSTANTONS IN QUANTUM GRAVITY 418
NONLINEAR DYNAMICS OF PATH INTEGRALS 425
4.1 SUM OVER HISTORIES 425
4.1.1 INTUITION BEHIND A PATH INTEGRAL 426
4.1.2 BASIC PATH-INTEGRAL CALCULATIONS 437
4.1.3 BRIEF HISTORY OF FEYNMAN S PATH INTEGRAL 445
4.1.4 PATH-INTEGRAL QUANTIZATION 452
4.1.5 STATISTICAL MECHANICS VIA PATH INTEGRALS 460
4.1.6 PATH INTEGRALS AND GREEN S FUNCTIONS 462
4.1.7 MONTE CARLO SIMULATION OF THE PATH INTEGRAL 468
4.2 SUM OVER GEOMETRIES AND TOPOLOGIES 474
4.2.1 SIMPLICIAL QUANTUM GEOMETRY 475
4.2.2 DISCRETE GRAVITATIONAL PATH INTEGRALS 477
4.2.3 REGGE CALCULUS 479
4.2.4 LORENTZIAN PATH INTEGRAL 481
4.2.5 NON-PERTURBATIVE QUANTUM GRAVITY 486
IMAGE 4
XIV CONTENTS
4.3 DYNAMICS OF FIELDS AND STRINGS 511
4.3.1 TOPOLOGICAL QUANTUM FIELD THEORY 511
4.3.2 TQFT AND SEIBERG-WITTEN THEORY 515
4.3.3 STRINGY ACTIONS AND AMPLITUDES 528
4.3.4 TRANSITION AMPLITUDES FOR STRINGS 532
4.3.5 WEYL INVARIANCE AND VERTEX OPERATOR FORMULATION 535 4.3.6 MORE
GENERAL STRINGY ACTIONS 535
4.3.7 TRANSITION AMPLITUDE FOR A SINGLE POINT PARTICLE 536 4.3.8
WITTEN S OPEN STRING FIELD THEORY 537
4.3.9 TOPOLOGICAL STRINGS 554
4.3.10 GEOMETRICAL TRANSITIONS 569
4.3.11 TOPOLOGICAL STRINGS AND BLACK HOLE ATTRACTORS 572 4.4 CHAOS FIELD
THEORY 578
4.5 NON-PHYSICAL APPLICATIONS OF PATH INTEGRALS 580
4.5.1 STOCHASTIC OPTIMAL CONTROL 580
4.5.2 NONLINEAR DYNAMICS OF OPTION PRICING 584
4.5.3 DYNAMICS OF COMPLEX NETWORKS 594
4.5.4 PATH-INTEGRAL DYNAMICS OF NEURAL NETWORKS 596 4.5.5 CEREBELLUM AS
A NEURAL PATH-INTEGRAL 617
4.5.6 DISSIPATIVE QUANTUM BRAIN MODEL 623
4.5.7 ACTION-AMPLITUDE PSYCHODYNAMICS 637
4.5.8 JOINT ACTION PSYCHODYNAMICS 651
4.5.9 GENERAL ADAPTATION PSYCHODYNAMICS 654
5 COMPLEX NONLINEARITY: COMBINING IT ALL TOGETHER 657 5.1 GEOMETRICAL
DYNAMICS, HAMILTONIAN CHAOS, AND PHASE TRANSITIONS 657
5.2 TOPOLOGY AND PHASE TRANSITIONS 664
5.2.1 COMPUTATION OF THE EULER CHARACTERISTIC 666
5.2.2 TOPOLOGICAL HYPOTHESIS 668
5.3 A THEOREM ON TOPOLOGICAL ORIGIN OF PHASE TRANSITIONS 670 5.4 PHASE
TRANSITIONS, TOPOLOGY AND THE SPHERICAL MODEL 673 5.5 TOPOLOGY CHANGE
AND CAUSAL CONTINUITY 680
5.5.1 MORSE THEORY AND SURGERY 682
5.5.2 CAUSAL DISCONTINUITY 687
5.5.3 GENERAL 4D TOPOLOGY CHANGE 689
5.5.4 A BLACK HOLE EXAMPLE 690
5.5.5 TOPOLOGY CHANGE AND PATH INTEGRALS 692
5.6 HARD VS. SOFT COMPLEXITY: A BIO-MECHANICAL EXAMPLE 693 5.6.1
BIO-MECHANICAL COMPLEXITY 694
5.6.2 DYNAMICAL COMPLEXITY IN BIO-MECHANICS 697 5.6.3 CONTROL COMPLEXITY
IN BIO-MECHANICS 700
5.6.4 COMPUTATIONAL COMPLEXITY IN BIO-MECHANICS 705 5.6.5 SIMPLICITY,
PREDICTABILITY AND MACRO-ENTANGLEMENT .. . 706
IMAGE 5
CONTENTS XV
5.6.6 REDUCTION OF MECHANICAL DOF AND ASSOCIATED CONTROLLERS 707
5.6.7 SELF-ASSEMBLY, SYNCHRONIZATION AND RESOLUTION 709
REFERENCES 713
INDEX 831
|
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| dewey-ones | 003 - Systems |
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| dewey-search | 003.75 |
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| discipline | Physik Allgemeines Informatik Mathematik |
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| id | DE-604.BV039726124 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:09:49Z |
| institution | BVB |
| isbn | 9783540793564 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024574115 |
| oclc_num | 225449456 |
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| owner | DE-19 DE-BY-UBM DE-20 |
| owner_facet | DE-19 DE-BY-UBM DE-20 |
| physical | XV, 844 S. graph. Darst. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Understanding complex systems Springer complexity |
| spelling | Ivancevic, Vladimir G. Verfasser aut Complex nonlinearity chaos, phase transitions, topology change and path integrals Vladimir G. Ivancevic ; Tijana T. Ivancevic Berlin ; Heidelberg Springer 2008 XV, 844 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Understanding complex systems Springer complexity Literaturverz. S. 713 - 830 Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Komplexes System (DE-588)4114261-5 gnd rswk-swf Komplexes System (DE-588)4114261-5 s Nichtlineare Dynamik (DE-588)4126141-0 s DE-604 Ivancevic, Tijana T. Verfasser aut Erscheint auch als Online-Ausgabe Complex nonlinearity DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024574115&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ivancevic, Vladimir G. Ivancevic, Tijana T. Complex nonlinearity chaos, phase transitions, topology change and path integrals Nichtlineare Dynamik (DE-588)4126141-0 gnd Komplexes System (DE-588)4114261-5 gnd |
| subject_GND | (DE-588)4126141-0 (DE-588)4114261-5 |
| title | Complex nonlinearity chaos, phase transitions, topology change and path integrals |
| title_auth | Complex nonlinearity chaos, phase transitions, topology change and path integrals |
| title_exact_search | Complex nonlinearity chaos, phase transitions, topology change and path integrals |
| title_full | Complex nonlinearity chaos, phase transitions, topology change and path integrals Vladimir G. Ivancevic ; Tijana T. Ivancevic |
| title_fullStr | Complex nonlinearity chaos, phase transitions, topology change and path integrals Vladimir G. Ivancevic ; Tijana T. Ivancevic |
| title_full_unstemmed | Complex nonlinearity chaos, phase transitions, topology change and path integrals Vladimir G. Ivancevic ; Tijana T. Ivancevic |
| title_short | Complex nonlinearity |
| title_sort | complex nonlinearity chaos phase transitions topology change and path integrals |
| title_sub | chaos, phase transitions, topology change and path integrals |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd Komplexes System (DE-588)4114261-5 gnd |
| topic_facet | Nichtlineare Dynamik Komplexes System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024574115&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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