An exploration of chaos: an introduction for natural scientists and engineers
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
North-Holland
1994
|
| Series: | Texts on computational mechanics
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 751 S. Ill., graph. Darst. |
| ISBN: | 0444820027 0444820035 |
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Record in the Search Index
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| adam_text | AN EXPLORATION OF CHAOS JOHN ARGYRIS GUNTER FAUST MARIA HAASE AN
INTRODUCTION FOR NATURAL SCIENTISTS AND ENGINEERS **+1 1994
NORTH-HOLLAND AMSTERDAM * LONDON * NEW YORK * TOKYO XVII TABLE OF
CONTENTS PREFACE VII 1 DESCRIPTIVE CONSPECTUS OF THE TEXT I 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 36 3.1 LINEAR AUTONOMOUS SYSTEMS 36 3.2 NON-LINEAR
SYSTEMS AND STABILITY 48 3.3 INVARIANT MANIFOLDS 55 3.4 DISCRETISATION
IN TIME 56 3.5 POINCARC MAP 58 3.6 FIXED POINTS AND CYCLES OF DISCRETE
SYSTEMS 61 3.7 AN EXAMPLE OF DISCRETE DYNAMICS - THE LOGISTIC MAP 65 4
DYNAMICAL SYSTEMS WITHOUT DISSIPATION 73 4.1 HAMILTON EQUATIONS FOR
CONSERVATIVE SYSTEMS 73 4.2 CANONICAL TRANSFORMATIONS, INTEGRABILITY 80
4.3 F-DIMENSIONAL TORI AND TRAJECTORIES 92 4.4 AN OUTLINE OF THE KAM
THEORY 94 4.5 UNSTABLE TORI, CHAOTIC REGIONS 100 4.6 A NUMERICAL
EXAMPLE: THE HENON MAP 110 5 DYNAMICAL SYSTEMS WITH DISSIPATION 127 5. 1
VOLUME CONTRACTION - A BASIC CHARACTERISTIC OF DISSIPATIVE SYSTEMS 127
5.2 STRANGE ATTRACTOR: LORENZ ATTRACTOR 131 5.3 POWER SPECTRUM AND
AUTOCORRELATION 136 5.3.1 HARMONIC ANALYSIS AND FOURIER TRANSFORMATION
136 5.3.2 CHARACTERISTICS OF THE FOURIER TRANSFORMATION; CONVOLUTIONS
AND CORRELATIONS 141 5.3.3 ELEMENTARY FOURIER TRANSFORMATIONS, LINE
SPECTRA, DIRAC ^ -FUNCTION 144 5.3.4 CHARACTERISATION OF ATTRACTORS WITH
THE HELP OF THE POWER SPECTRUM AND AUTOCORRELATION 148 5.4 LYAPUNOV
EXPONENTS 151 5.4.1 LINEAR STABILITY ANALYSIS OF NON-LINEAR SYSTEMS:
STATE OF EQUILIBRIUM 152 XVIII TABLE OF CONTENTS 5.4.2 STABILITY OF
PERIODIC SOLUTIONS: FLOQUET THEORY 158 5.4.3 LYAPUNOV EXPONENT OF
ONE-DIMENSIONAL MAPS 169 5.4.4 LYAPUNOV EXPONENTS OF N-DIMENSIONAL
CONTINUOUS SYSTEMS 173 5.4.5 LYAPUNOV EXPONENTS OF N-DIMENSIONAL
DISCRETE SYSTEMS ... 180 5.4.6 NUMERICAL CALCULATION OF LYAPUNOV
EXPONENTS 182 5.5 DIMENSIONS 189 5.5.1 CANTOR SET 191 5.5.2 FRACTAL
DIMENSIONS: CAPACITY DIMENSION AND HAUSDORFF-BESICOVITCH DIMENSION 195
5.5.3 INFORMATION DIMENSION 197 5.5.4 CORRELATION DIMENSION, POINTWISE
DIMENSION AND RECONSTRUCTION OF ATTRACTORS 210 5.5.5 GENERALISED
DIMENSION D 4 225 5.5.6 LYAPUNOV DIMENSION AND KAPLAN-YORKE CONJECTURE
227 5.6 KOLNIOGOROV-SINAI ENTROPY 233 5.6.1 THE BERNOULLI SHIFT 234
5.6.2 DEFINITION OF KS ENTROPY 238 5.6.3 LINK BETWEEN KS ENTROPY AND
LYAPUNOV EXPONENTS 244 5.6.4 TIME SPAN FOR RELIABLE PROGNOSES 247 6
LOCAL BIFURCATION THEORY 250 6.1 MOTIVATION 251 6.2 CENTRE MANIFOLD 259
6.3 NORMAL FORMS 280 6.4 NORMAL FORMS OF BIFURCATIONS FOR ONE-PARAMETRIC
FLOWS 294 6.5 STABILITY OF BIFURCATIONS SUBJECT TO PERTURBATIONS 315 6.6
BIFURCATIONS OF THE FIXED POINTS OF ONE-PARAMETRIC MAPS 320 6.7
RENORMALISATION AND SELF-SIMILARITY WITH THE EXAMPLE OF THE LOGISTIC MAP
346 6.7.1 THE MECHANISM OF PERIOD DOUBLINGS AD INFINITUM 346 6.7.2
SUPERSTABLE CYCLES 354 6.7.3 SELF-SIMILARITY IN THE X-SPACE 358 6.7.4
SELF-SIMILARITY IN THE PARAMETER SPACE 369 6.7.5 LINK WITH SECOND-ORDER
PHASE TRANSITIONS AND RENORMALISATION METHODS 383 6.8 A DESCRIPTIVE
INTRODUCTION TO SYNERGETICS 388 7 CONVECTION FLOWS: BENARD PROBLEM 421
7.1 BASIC HYDRODYNAMIC EQUATIONS 426 7.2 BOUSSINESQ-OBERBECK
APPROXIMATION 438 7.3 LORENZ MODEL 440 7.4 EVOLUTION OF THE LORENZ
SYSTEM 446 8 ROUTES TO TURBULENCE 458 8.1 LANDAU SCENARIO 462 8.2
RUELLE-TAKENS SCENARIO 467 TABLE OF CONTENTS XIX 8.2.1 INSTABILITY OF
QUASI-PERIODIC MOTIONS ON THE 3D TORUS .... 468 8.2.2 EXPERIMENTS OF
GOLLUB AND SWINNEY 472 8.3 UNIVERSAL CHARACTERISTICS OF THE TRANSITION
FROM QUASI-PERIODICITY TO CHAOS 476 8.3.1 THE IMPULSIVELY EXCITED DAMPED
OSCILLATOR 476 8.3.2 THE ONE-DIMENSIONAL CIRCLE MAP 480 8.3.3 SCALING
CHARACTERISTICS OF THE CIRCLE MAP 491 8.3.3.1 LOCAL SCALING LAWS 491
8.3.3.2 GLOBAL SCALING LAWS 503 8.4 THE FEIGENBAUM ROUTE TO CHAOS VIA
PERIOD DOUBLINGS 509 8.4.1 FURTHER SCALING CHARACTERISTICS OF THE PERIOD
DOUBLING CASCADE 511 8.4.2 EXPERIMENTAL VALIDATION OF THE FEIGENBAUM
ROUTE 524 8.5 QUASI-PERIODIC TRANSITION FOR A FIXED WINDING NUMBER 528
8.5.1 SCALING CHARACTERISTICS OF THE QUASI-PERIODIC TRANSITION . . . 529
8.5.2 EXPERIMENTAL VALIDATION OF THE QUASI-PERIODIC TRANSITION .. 542
8.6 THE ROUTE TO CHAOS VIA INTERMITTENCY 548 8.6.1 INTERMITTENCY IN THE
LOGISTIC MAP 549 8.6.2 CLASSIFICATION OF INTERMITTENCY 554 8.6.3 TYPE I
INTERMITTENCY 556 8.6.4 TYPE III INTERMITTENCY 564 8.6.5 TYPE II
INTERMITTENCY 570 8.7 ROUTES OUT OF CHAOS, CONTROL OF CHAOS 572 9
COMPUTER EXPERIMENTS 576 9.1 INTRODUCTION TO BONE REMODELLING PROCESSES
579 9.2 HENON MAP 595 9.3 THE LORENZ SYSTEM REVISITED 601 9.4 VAN DER
POL EQUATION 608 9.4.1 SELF-SUSTAINED OSCILLATION WITHOUT EXTERNAL
EXCITATION 609 9.4.2 SELF-SUSTAINED OSCILLATION WITH EXTERNAL EXCITATION
615 9.5 DUFFING EQUATION 631 9.6 .JULIA SETS AND THEIR ORDERING
PRINCIPLE 653 9.7 MORPHOLOGY OF THE ARNOL D TONGUES 667 9.8 OSCILLATORY
KINETICS OF CHEMICAL REACTIONS ON SOLID SURFACES 676 9.8.1 AN
ELECTROCHEMICAL SYSTEM: A PT WIRE IN A SOLUTION CONTAINING DISSOLVED CU
2+ AND OTHER IONS 677 9.8.2 PRELIMINARIES TO THE KINETICS IN THE
CATALYTIC OXIDATION OF CO ON PT(110) 679 9.8.3 FORMULATION OF THE
KINETIC MODEL 687 9.8.4 ADDITIONAL INFORMATION ON OSCILLATORY KINETIC
STATES 690 9.8.5 MIXED-MODE OSCILLATIONS 691 9.8.6 ON AN IDENTIFICATION
OF CHAOS AND HYPERCHAOS IN KINETIC SURFACE REACTIONS 692 9.8.7
SPATIO-TEMPORAL EVOLUTION OF PATTERNS 696 XX TABLE OF CONTENTS 9.9 AN
APERGU OF CHAOTIC BEHAVIOUR IN OUR SOLAR SYSTEM 703 9.9.1 ON THE
TUMBLING MOTION OF HYPERION 704 9.9.2 FURTHER COMMENTS ON OUT-OF-ROUND
SATELLITES 711 9.9.3 THE 3:1 KIRKWOOD GAP 713 COLOR PLATES 397
BIBLIOGRAPHY 721 INDEX 739
|
| any_adam_object | 1 |
| author | Argyris, John H. 1913-2004 Faust, Gunter Haase, Maria |
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| dewey-sort | 13.75 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Physik Informatik |
| format | Book |
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| id | DE-604.BV011105233 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:04:04Z |
| institution | BVB |
| isbn | 0444820027 0444820035 |
| language | English |
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| physical | XX, 751 S. Ill., graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | North-Holland |
| record_format | marc |
| series | Texts on computational mechanics |
| series2 | Texts on computational mechanics |
| spelling | Argyris, John H. 1913-2004 Verfasser (DE-588)107323893 aut An exploration of chaos an introduction for natural scientists and engineers John Argyris ; Gunter Faust ; Maria Haase Amsterdam [u.a.] North-Holland 1994 XX, 751 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts on computational mechanics 7 Chaostheorie (DE-588)4009754-7 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Chaostheorie (DE-588)4009754-7 s DE-604 Nichtlineare Dynamik (DE-588)4126141-0 s 1\p DE-604 Faust, Gunter Verfasser aut Haase, Maria Verfasser aut Texts on computational mechanics 7 (DE-604)BV005099466 7 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007440384&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Argyris, John H. 1913-2004 Faust, Gunter Haase, Maria An exploration of chaos an introduction for natural scientists and engineers Texts on computational mechanics Chaostheorie (DE-588)4009754-7 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4126141-0 |
| title | An exploration of chaos an introduction for natural scientists and engineers |
| title_auth | An exploration of chaos an introduction for natural scientists and engineers |
| title_exact_search | An exploration of chaos an introduction for natural scientists and engineers |
| title_full | An exploration of chaos an introduction for natural scientists and engineers John Argyris ; Gunter Faust ; Maria Haase |
| title_fullStr | An exploration of chaos an introduction for natural scientists and engineers John Argyris ; Gunter Faust ; Maria Haase |
| title_full_unstemmed | An exploration of chaos an introduction for natural scientists and engineers John Argyris ; Gunter Faust ; Maria Haase |
| title_short | An exploration of chaos |
| title_sort | an exploration of chaos an introduction for natural scientists and engineers |
| title_sub | an introduction for natural scientists and engineers |
| topic | Chaostheorie (DE-588)4009754-7 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| topic_facet | Chaostheorie Nichtlineare Dynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007440384&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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