An exploration of dynamical systems and chaos:
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| Main Authors: | , , , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Heidelberg ; New York ; Dordrecht ; London
Springer
[2015]
|
| Edition: | Completely revised and enlarged second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXII, 865 Seiten Illustrationen, Diagramme |
| ISBN: | 3662460416 9783662460412 9783662460429 |
Staff View
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| 100 | 1 | |a Argyris, John H. |d 1913-2004 |e Verfasser |0 (DE-588)107323893 |4 aut | |
| 240 | 1 | 0 | |0 (DE-588)1079623914 |a Die Erforschung des Chaos |
| 245 | 1 | 0 | |a An exploration of dynamical systems and chaos |c John Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich |
| 250 | |a Completely revised and enlarged second edition | ||
| 264 | 1 | |a Heidelberg ; New York ; Dordrecht ; London |b Springer |c [2015] | |
| 300 | |a XXII, 865 Seiten |b Illustrationen, Diagramme | ||
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| 653 | |a Research | ||
| 653 | |a Chaos | ||
| 653 | |a Dynamical Systems | ||
| 653 | |a Kolmogorov-Sinai Entropy | ||
| 653 | |a Lorenz-Model | ||
| 653 | |a Lyapunov-Exponents | ||
| 653 | |a Turbulence | ||
| 653 | |a Routes to Chaos | ||
| 653 | |a Fractal Dimensions | ||
| 653 | |a Conservative und Dissipative Systems | ||
| 653 | |a Local Bifurcations | ||
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| 700 | 1 | |a Haase, Maria |e Verfasser |0 (DE-588)1144653487 |4 aut | |
| 700 | 1 | |a Friedrich, Rudolf |d 1956-2012 |e Verfasser |0 (DE-588)1017600031 |4 aut | |
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CONTENTS
1 DESCRIPTIVE SYNOPSIS OF THE TEXT 1
2 PRELIMINARIES 13
2.1 CAUSALITY - DETERMINISM 14
2.2 DYNAMICAL SYSTEMS - EXAMPLES 21
2.3 PHASE SPACE 28
2.4 FIRST INTEGRALS AND MANIFOLDS 30
2.5 QUALITATIVE AND QUANTITATIVE APPROACH 34
3 MATHEMATICAL INTRODUCTION TO DYNAMICAL SYSTEMS 35
3.1 LINEAR AUTONOMOUS SYSTEMS 35
3.2 NON-LINEAR SYSTEMS AND STABILITY 47
3.3 INVARIANT MANIFOLDS 53
3.4 DISCRETISATION IN TIME 55
3.5 POINCARE MAP 57
3.6 FIXED POINTS AND CYCLES OF DISCRETE SYSTEMS 59
3.7 AN EXAMPLE OF DISCRETE DYNAMICS - THE LOGISTIC MAP 63
3.8 FOURIER SERIES AND FOURIER TRANSFORM 70
3.8.1 FOURIER SERIES 70
3.8.2 FOURIER INTEGRAL AND FOURIER TRANSFORM 73
3.8.3 CHARACTERISTICS OF THE FOURIER TRANSFORM 75
3.8.4 ELEMENTARY FOURIER TRANSFORM, LINE SPECTRA,
DIRAC 5-FUNCTION 79
3.8.5 WAVELET TRANSFORM 83
3.9 BASIC CONCEPTS OF PROBABILITY THEORY 86
3.9.1 EXPERIMENT WITH RANDOM OUTCOME 87
3.9.2 RANDOM VARIABLES 90
3.9.3 PROBABILITY 90
3.9.4 CONDITIONAL PROBABILITY AND JOINT PROBABILITY 95
3.9.5 DISTRIBUTION FUNCTION AND PROBABILITY DENSITY FUNCTION . 97
3.9.6 CHARACTERISTIC VALUES OF A DISTRIBUTION 101
3.9.7 INDEPENDENT AND DEPENDENT EVENTS 104
3.9.8 MOMENT-GENERATING AND CHARACTERISTIC FUNCTIONS 106
3.9.9 SPECIAL PROBABILITY DISTRIBUTIONS 109
3.9.10 CENTRAL LIMIT THEOREM 116
3.9.11 CAUCHY DISTRIBUTION AND A-STABLE LEVY DISTRIBUTION 120
HTTP://D-NB.INFO/106318990X
XVIII
CONTENTS
3.9.12 ANALYSIS OF STOCHASTIC PROCESSES 126
3.10 INVARIANT MEASURE AND ERGODIC ORBITS 130
3.10.1 NATURAL INVARIANT DENSITY OF THE LOGISTIC MAP 130
3.10.2 FROBENIUS-PERRON EQUATION AND ERGODICITY 135
4 DYNAMICAL SYSTEMS WITHOUT DISSIPATION 139
4.1 HAMILTON EQUATIONS FOR CONSERVATIVE SYSTEMS 139
4.2 CANONICAL TRANSFORMATIONS, INTEGRABILITY 145
4.3 F-DIMENSIONAL TORI AND TRAJECTORIES 155
4.4 AN OUTLINE OF THE KAM THEORY 158
4.5 UNSTABLE TORI. CHAOTIC REGIONS 163
4.6 A NUMERICAL EXAMPLE: THE HENON MAP 172
5 DYNAMICAL SYSTEMS WITH DISSIPATION 189
5.1 VOLUME CONTRACTION - A BASIC CHARACTERISTIC OF DISSIPATIVE
SYSTEMS 190
5.2 STRANGE ATTRACTOR: LORENZ ATTRACTOR 192
5.3 POWER SPECTRUM AND AUTOCORRELATION 200
5.4 LYAPUNOV EXPONENTS 205
5.4.1 LINEAR STABILITY ANALYSIS OF NON-LINEAR SYSTEMS:
STATE OF EQUILIBRIUM 205
5.4.2 STABILITY OF PERIODIC SOLUTIONS: FLOQUET THEORY 211
5.4.3 LYAPUNOV EXPONENT OF ONE-DIMENSIONAL MAPS 221
5.4.4 LYAPUNOV EXPONENTS OF N-DIMENSIONAL CONTINUOUS
SYSTEMS 224
5.4.5 LYAPUNOV EXPONENTS OF N-DIMENSIONAL DISCRETE SYSTEMS . . . 231
5.4.6 NUMERICAL CALCULATION OF LYAPUNOV EXPONENTS 232
5.5 DIMENSIONS 238
5.5.1 CANTOR SET 240
5.5.2 FRACTAL DIMENSIONS: CAPACITY DIMENSION AND
HAUSDORFF-BESICOVITCH DIMENSION 244
5.5.3 INFORMATION DIMENSION 246
5.5.4 CORRELATION DIMENSION, POINTWISE DIMENSION AND
RECONSTRUCTION OF ATTRACTORS 258
5.5.5 GENERALISED DIMENSION D
Q
274
5.5.6 LYAPUNOV DIMENSION AND KAPLAN-YORKE CONJECTURE 276
5.6 KOHNOGOROV-SINAI ENTROPY 281
5.6.1 THE BERNOULLI SHIFT 283
5.6.2 DEFINITION OF KS ENTROPY 287
5.6.3 LINK BETWEEN KS ENTROPY AND LYAPUNOV EXPONENTS 293
5.6.4 TIME SPAN FOR RELIABLE PROGNOSES 296
6 LOCAL BIFURCATION THEORY 299
6.1 MOTIVATION 301
6.2 CENTRE MANIFOLD 308
6.3 NORMAL FORMS 328
CONTENTS XIX
6.4 NORMAL FORMS OF BIFURCATIONS FOR ONE-PARAMETRIC FLOWS 340
6.5 STABILITY OF BIFURCATIONS SUBJECT TO PERTURBATIONS 360
6.6 BIFURCATIONS OF THE FIXED POINTS OF ONE-PARAMETRIC MAPS 364
6.7 RENORMALISATION AND SELF-SIMILARITY WITH THE EXAMPLE OF THE
LOGISTIC MAP 387
6.7.1 THE MECHANISM OF PERIOD DOUBLINGS AD INFINITUM 387
6.7.2 SUPERSTABLE CYCLES 393
6.7.3 SELF-SIMILARITY IN THE X-SPACE 398
6.7.4 SELF-SIMILARITY IN THE PARAMETER SPACE 409
6.7.5 LINK WITH SECOND-ORDER PHASE TRANSITIONS AND
RENORMALISATION METHODS 422
6.8 A DESCRIPTIVE INTRODUCTION TO SYNERGETICS 426
7 CONVECTIVE FLOW: BENARD PROBLEM 435
7.1 BASIC HYDRODYNAMIC EQUATIONS 441
7.2 BOUSSINESQ-OBERBECK APPROXIMATION 451
7.3 LORENZ MODEL 453
7.4 EVOLUTION OF THE LORENZ SYSTEM 459
8 ROUTES TO CHAOS 473
8.1 LANDAU SCENARIO 473
8.2 RUELLE-TAKENS SCENARIO 478
8.2.1 INSTABILITY OF QUASI-PERIODIC MOTIONS ON THE 3D TORUS 478
8.2.2 EXPERIMENTS OF GOLLUB AND SWINNEY 483
8.3 UNIVERSAL CHARACTERISTICS OF THE TRANSITION FROM QUASI-PERIODICITY
TO CHAOS 486
8.3.1 THE KICKED ROTATOR WITH DAMPING 487
8.3.2 THE ONE-DIMENSIONAL CIRCLE MAP 490
8.3.3 SCALING CHARACTERISTICS OF THE CIRCLE MAP 502
8.3.3.1 LOCAL SCALING LAWS 502
8.3.3.2 GLOBAL SCALING LAWS 514
8.4 THE FEIGENBAUM ROUTE TO CHAOS VIA PERIOD DOUBLINGS 520
8.4.1 FURTHER SCALING CHARACTERISTICS OF THE PERIOD DOUBLING
CASCADE 523
8.4.2 EXPERIMENTAL VALIDATION OF THE FEIGENBAUM ROUTE 534
8.5 QUASI-PERIODIC TRANSITION FOR A FIXED ROTATION NUMBER 538
8.5.1 SCALING CHARACTERISTICS OF THE QUASI-PERIODIC TRANSITION . 539
8.5.2 MULTIFRACTAL STRUCTURES 545
8.5.3 EXPERIMENTAL VALIDATION OF THE QUASI-PERIODIC TRANSITION . . . 554
8.6 THE ROUTE TO CHAOS VIA INTERMITTENCY 561
8.6.1 INTERMITTENCY IN THE LOGISTIC MAP 562
8.6.2 CLASSIFICATION OF INTERMITTENCY 567
8.6.3 TYPE I INTERMITTENCY 569
8.6.4 TYPE III INTERMITTENCY 577
8.6.5 TYPE II INTERMITTENCY 582
XX
CONTENTS
8.7 ROUTES OUT OF CHAOS, CONTROL OF CHAOS 586
8.7.1 CONTROL OF CHAOS WITHOUT FEEDBACK 588
8.7.2 CONTROL OF CHAOS WITH FEEDBACK 589
9 TURBULENCE 593
9.1 DYNAMICS OF INCOMPRESSIBLE FLUIDS 597
9.1.1 THE BASIC HYDRODYNAMIC EQUATIONS 598
9.1.2 THE LOCAL ENERGY DISSIPATION RATE 600
9.1.3 THE VORTICITY EQUATION 602
9.1.4 THE LAGRANGIAN DESCRIPTION OF FLUID FLOWS 607
9.1.5 HYDRODYNAMIC VORTICES 611
9.1.5.1 LAMB-OSEEN VORTEX 611
9.1.5.2 STRETCHED VORTEX 613
9.1.5.3 LUNDGREN VORTEX 616
9.2 FROM CHAOS TO TURBULENCE 616
9.2.1 CHAOS IN FLUID FLOWS 616
9.2.2 DYNAMICS OF POINT VORTICES IN TWO-DIMENSIONAL IDEAL
FLOWS 616
9.2.2.1 THE HAMILTONIAN CHARACTER OF THE POINT VORTEX
DYNAMICS 618
9.2.2.2 TWO POINT VORTICES 620
9.2.2.3 THREE POINT VORTICES 621
9.2.2.4 FOUR POINT VORTICES 626
9.2.2.5 MIXING BY POINT VORTICES 628
9.2.3 ONSAGER'S EQUILIBRIUM THEORY 628
9.2.3.1 VISCOSITY 629
9.3 TURBULENCE: DETERMINISM AND STOCLIASTICITY 630
9.3.1 STATISTICAL AVERAGING 630
9.3.2 MOMENT EQUATIONS: THE CLOSURE PROBLEM OF TURBULENCE . 632
9.3.3 DECAYING TURBULENCE 632
9.3.4 REYNOLDS EQUATION AND TURBULENCE MODELLING 633
9.4 CHARACTERISTIC SCALES OF TURBULENCE 635
9.4.1 TAYLOR HYPOTHESIS 635
9.4.2 PHENOMENOLOGY OF EDDY DECAY AND ENERGY CASCADE 636
9.4.3 THE INTEGRAL LENGTH L 637
9.4.4 THE KOLMOGOROV MICROSCALES 637
9.4.5 THE TAYLOR LENGTH 638
9.4.6 THE TAYLOR-REYNOLDS NUMBER 638
9.5 THE TURBULENT CASCADE 639
9.5.1 THE VON KARMAN-HOWARTLI RELATION 639
9.5.2 THE ENERGY SPECTRUM E{K) 641
9.5.3 THE ENERGY CASCADE IN THREE-DIMENSIONAL TURBULENCE 643
9.5.4 HEISENBERG'S THEORY 644
CONTENTS XXI
9.6 KOLMOGOROV'S THEORY OF LOCALLY ISOTROPIC TURBULENCE 646
9.6.1 EVOLUTION EQUATION OF THE VELOCITY INCREMENTS 646
9.6.2 THE ENERGY BALANCE OF THE VELOCITY INCREMENT 647
9.6.3 THE AVERAGED ENERGY BALANCE EQUATION 649
9.6.3.1 HOMOGENEOUS TURBULENCE 649
9.6.3.2 HOMOGENEOUS ISOTROPIC TURBULENCE 650
9.6.3.3 KOLMOGOROV'S -4/5 LAW 650
9.6.3.4 DISSIPATION RANGE 651
9.6.3.5 INERTIAL RANGE 652
9.6.4 KOLMOGOROV'S K41 THEORY 652
9.6.4.1 UNIVERSALITY OF THE STATISTICS OF SMALL-SCALE
TURBULENCE 653
9.6.4.2 SELF-SIMILAR BEHAVIOUR IN THE INERTIAL RANGE 653
9.6.4.3 SELF-SIMILARITY AND FRACTAL SCALING LAWS 654
9.6.4.4 EXPERIMENTAL TESTING OF THE SELF-SIMILARITY
HYPOTHESIS 655
9.6.5 THE PHENOMENON OF INTERMITTENCY 657
9.6.6 KOLMOGOROV K62 657
9.6.7 MULTIFRACTAL MODEL 660
9.6.8 MULTISCALING STATISTICS 662
9.7 OUTLOOK 668
9.8 APPENDIX: ISOTROPIC TENSOR FIELDS 669
9.8.1 LONGITUDINAL AND TRANSVERSAL CORRELATION FUNCTIONS 671
9.8.1.1 THE CORRELATION FUNCTION OF THIRD ORDER 672
9.8.2 CORRELATION FUNCTIONS FOR INCOMPRESSIBLE, ISOTROPIC AND
HOMOGENEOUS FIELDS 673
9.8.2.1 THE CORRELATION FUNCTIONS OF SECOND ORDER 673
9.8.2.2 THE CORRELATION FUNCTIONS OF THIRD ORDER 673
9.8.3 STRUCTURE FUNCTIONS OF INCOMPRESSIBLE FIELDS 674
9.8.3.1 STRUCTURE FUNCTION OF SECOND ORDER 674
9.8.3.2 STRUCTURE FUNCTION OF THIRD ORDER 675
10 COMPUTER EXPERIMENTS 677
10.1 INTRODUCTION TO BONE REMODELLING PROCESSES 680
10.2 HENON MAP 698
10.3 THE LORENZ SYSTEM REVISITED 707
10.4 VAN DER POL EQUATION 715
10.4.1 SELF-EXCITED OSCILLATION 715
10.4.2 DRIVEN VAN DER POL OSCILLATOR 721
10.5 DUFFING EQUATION 737
10.6 SHILNIKOV BIFURCATIONS 762
10.7 JULIA SETS AND THEIR ORDERING PRINCIPLE 771
10.8 MORPHOLOGY OF THE ARNOLD TONGUES 788
XXII CONTENTS
10.9 OSCILLATORY KINETICS OF CHEMICAL REACTIONS ON SINGLE-CRYSTAL
SURFACES 798
10.9.1 OXIDATION OF HYDROGEN ON A PLATINUM ELECTRODE 799
10.9.2 KINETICS OF THE CATALYTIC OXIDATION OF CO ON PT(110) 801
10.9.2.1 PHENOMENOLOGY OF CATALYTIC OXIDATION 802
10.9.2.2 STEP BY STEP FORMULATION OF A KINETIC MODEL 805
10.9.3 IDENTIFICATION OF CHAOS AND HYPERCHAOS IN KINETIC SURFACE
REACTIONS 812
10.9.4 SPATIO-TEMPORAL PATTERN FORMATION 815
REFERENCES 823
INDEX 849 |
| any_adam_object | 1 |
| author | Argyris, John H. 1913-2004 Faust, Gunter Haase, Maria Friedrich, Rudolf 1956-2012 |
| author_GND | (DE-588)107323893 (DE-588)1144653169 (DE-588)1144653487 (DE-588)1017600031 |
| author_facet | Argyris, John H. 1913-2004 Faust, Gunter Haase, Maria Friedrich, Rudolf 1956-2012 |
| author_role | aut aut aut aut |
| author_sort | Argyris, John H. 1913-2004 |
| author_variant | j h a jh jha g f gf m h mh r f rf |
| building | Verbundindex |
| bvnumber | BV043302721 |
| classification_rvk | UG 3900 |
| ctrlnum | (OCoLC)898296395 (DE-599)DNB106318990X |
| dewey-full | 530.15539 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15539 |
| dewey-search | 530.15539 |
| dewey-sort | 3530.15539 |
| dewey-tens | 530 - Physics |
| discipline | Maschinenbau / Maschinenwesen Physik Mathematik |
| edition | Completely revised and enlarged second edition |
| format | Book |
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| id | DE-604.BV043302721 |
| illustrated | Illustrated |
| indexdate | 2024-09-10T01:58:24Z |
| institution | BVB |
| isbn | 3662460416 9783662460412 9783662460429 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028723556 |
| oclc_num | 898296395 |
| open_access_boolean | |
| owner | DE-29T DE-83 DE-703 DE-19 DE-BY-UBM |
| owner_facet | DE-29T DE-83 DE-703 DE-19 DE-BY-UBM |
| physical | XXII, 865 Seiten Illustrationen, Diagramme |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer |
| record_format | marc |
| spelling | Argyris, John H. 1913-2004 Verfasser (DE-588)107323893 aut (DE-588)1079623914 Die Erforschung des Chaos An exploration of dynamical systems and chaos John Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich Completely revised and enlarged second edition Heidelberg ; New York ; Dordrecht ; London Springer [2015] XXII, 865 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Research Chaos Dynamical Systems Kolmogorov-Sinai Entropy Lorenz-Model Lyapunov-Exponents Turbulence Routes to Chaos Fractal Dimensions Conservative und Dissipative Systems Local Bifurcations Nonlinear Dynamics Strange Attractors Chaostheorie (DE-588)4009754-7 s DNB Nichtlineare Dynamik (DE-588)4126141-0 s Faust, Gunter Verfasser (DE-588)1144653169 aut Haase, Maria Verfasser (DE-588)1144653487 aut Friedrich, Rudolf 1956-2012 Verfasser (DE-588)1017600031 aut Erscheint auch als Online-Ausgabe An exploration of dynamical systems and chaos B:DE-101 application/pdf http://d-nb.info/106318990X/04 Inhaltsverzeichnis X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5096101&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028723556&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Argyris, John H. 1913-2004 Faust, Gunter Haase, Maria Friedrich, Rudolf 1956-2012 An exploration of dynamical systems and chaos Nichtlineare Dynamik (DE-588)4126141-0 gnd Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4126141-0 (DE-588)4009754-7 |
| title | An exploration of dynamical systems and chaos |
| title_GND | (DE-588)1079623914 |
| title_alt | Die Erforschung des Chaos |
| title_auth | An exploration of dynamical systems and chaos |
| title_exact_search | An exploration of dynamical systems and chaos |
| title_full | An exploration of dynamical systems and chaos John Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich |
| title_fullStr | An exploration of dynamical systems and chaos John Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich |
| title_full_unstemmed | An exploration of dynamical systems and chaos John Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich |
| title_short | An exploration of dynamical systems and chaos |
| title_sort | an exploration of dynamical systems and chaos |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | Nichtlineare Dynamik Chaostheorie |
| url | http://d-nb.info/106318990X/04 http://deposit.dnb.de/cgi-bin/dokserv?id=5096101&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028723556&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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