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Chaos theory tamed:

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Bibliographic Details
Main Author:	Williams, Garnett P. (Author)
Format:	Book
Language:	English
Published:	London Taylor & Francis 1997
Subjects:	Chaos (théorie des systèmes) Chaos Dynamische systemen Chaotic behavior in systems Chaostheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	XVII, 499 S. graph. Darst.
ISBN:	0748407499

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adam_text	CHAOS THEORY TAMED GAMETT P. WILLIAMS US GEOLOGICAL SURVEY (RET.) TAYLOR &FRANCIS J PUBLISHERS SINRE 17QX CONTENTS PREFACE XI SYMBOLS XV PART I BACKGROUND 1 1 INTRODUCTION 3 SUMMARY 7 2 CHAOS IN PERSPECTIVE 9 WHERE CHAOS OCCURS 9 CAUSES OF CHAOS 13 BENEFITS OF ANALYZING FOR CHAOS 14 CONTRIBUTIONS OF CHAOS THEORY 15 HISTORICAL DEVELOPMENT 17 SUMMARY 19 PART II THE AUXILIARY TOOLKIT 21 3 PHASE SPACE*THE PLAYING FIELD 23 STANDARD PHASE SPACE 24 PSEUDO (LAGGED) PHASE SPACE . 27 SUMMARY 32 4 DISTANCES AND LINES IN SPACE 35 STRAIGHT-LINE DISTANCE BETWEEN TWO POINTS 35 GETTING THE PARAMETERS FOR A STRAIGHT-LINE EQUATION 37 INTERPOLATION 39 SUMMARY 46 CONTENTS 5 VECTORS 49 SCALARS AND VECTORS 49 COORDINATE VECTORS 50 VECTOR ADDITION AND SUBTRACTION 52 SCALAR MULTIPLICATION 54 THE DOT PRODUCT 55 THE ANGLE BETWEEN TWO VECTORS 56 ORTHOGONAIIZATION 58 UNIT VECTORS AND ORTHONORMALIZATION 62 SUMMARY 64 6 PROBABILITY AND INFORMATION 65 VARIATION 65 FREQUENCY AND PROBABILITY 67 ESTIMATING PROBABILITIES 70 PROBABILITIES INVOLVING TWO OR MORE VARIABLES 77 PROBABILITY AS THE CORE OF INFORMATION 86 SUMMARY 95 7 AUTOCORRELATION 97 AUTOCOVARIANCE 98 VARIANCE 101 AUTOCORRELATION FOR A GIVEN LAG 101 THE CORRELOGRAM 104 SUMMARY 104 8 FOURIER ANALYSIS 107 INTRODUCTION 107 WAVE RELATIONS 108 ADDING WAVES 111 HARMONICS 114 THE FOURIER SERIES 117 DISCRETE FOURIER COEFFICIENTS 119 VARIANCE (POWER) 121 GRAPHICAL DESCRIPTION (DOMAINS) OF SINUSOIDAL DATA 122 RECORDS OF INFINITE PERIOD AND THE FOURIER INTEGRAL 123 FOURIER TRANSFORM OF THE AUTOCORRELATION FUNCTION 125 DISCRETE FOURIER TRANSFORM 125 SAMPLE PERIODOGRAMS 126 SIZEOFDATASET 129 SAMPLING INTERVALS IN FOURIER ANALYSIS 129 CONCLUDING REMARKS 129 SUMMARY 130 VI CONTENTS 9 PRELIMINARY ANALYSIS OF TIME-SERIES DATA 131 REGULARITY OF TIME INTERVALS BETWEEN MEASUREMENTS 131 FIRST EXAMINATION OF DATA 131 REMOVING PERIODICITY AND TREND 133 SUMMARY 156 PART III HOW TO GET THERE FROM HERE 159 10 THE PARAMETER AS KING 161 THE LOGISTIC EQUATION 161 TERMINOLOGY 170 SUMMARY 173 11 NONCHAOTIC ATTRACTORS 175 ABOUT ATTRACTORS 175 POINT ATTRACTORS 177 PERIODIC ATTRACTORS (LIMIT CYCLES) 180 THE TORUS 182 SUMMARY 187 12 ROUTES TO CHAOS 189 PERIOD-DOUBLING 189 INTERMITTENCY 197 QUASIPERIODICITY 201 SUMMARY 202 13 CHAOTIC EQUATIONS 203 EQUATION REQUIREMENTS 203 SAMPLE EQUATIONS 205 SUMMARY 208 PART IV CHARACTERISTICS OF CHAOS 209 14 SENSITIVE DEPENDENCE ON INITIAL CONDITIONS 211 FROM TINY TO HUGE DIFFERENCES 212 COMPUTER INACCURACY AND IMPRECISION 214 INTERPRETATIONS 218 SUMMARY 219 CONTENTS 15 THE CHAOTIC (STRANGE) ATTRACTOR SIMILARITIES WITH OTHER ATTRACTORS INVARIANT PROBABILITY DISTRIBUTION OF ATTRACTOR DISTINCTIVE FEATURES OF CHAOTIC ATTRACTORS DEFINITIONS OF A CHAOTIC ATTRACTOR SUMMARY 16 ORDER WITHIN CHAOS WINDOWS ROUTES BETWEEN WINDOWS AND CHAOS THE CHAOTIC ATTRACTOR ZONES OF POPULARITY ON THE ATTRACTOR SELF-ORGANIZATION, COMPLEXITY, AND EMERGENT SYSTEMS SUMMARY 17 FRACTAL STRUCTURE DEFINITIONS FRACTALS AND CHAOS CHARACTERISTICS VALUE OF FRACTALS SUMMARY 221 222 222 226 227 227 229 229 231 232 233 233 235 237 237 238 241 242 243 PART V PHASE SPACE SIGNATURES 246 18 UNCOVERING DETERMINISM 247 POINCARE SECTIONS 247 RETURN MAPS 256 NEXT-AMPLITUDE (SUCCESSIVE-MAXIMA) PLOTS 258 DIFFERENCE PLOTS 260 SUMMARY 263 19 ATTRACTOR RECONSTRUCTION 265 GROWTH OF POINT DISTANCES IN EMBEDDED SPACE 266 SURROGATE DATA 267 TIME-DELAY METHOD 268 SINGULAR SYSTEM ANALYSIS 284 . SUMMARY 287 VLLL CONTENTS PART VI DIMENSIONS 289 20 BACKGROUND INFORMATION ON DIMENSIONS 291 CONCEPTS OF DIMENSION 291 TYPES AND IMPORTANCE OF EXPONENT DIMENSIONS 296 FRACTAL DIMENSION 298 SUMMARY 299 21 SIMILARITY DIMENSION 301 SCALING 301 SIMPLE GEOMETRIC FORMS AND THEIR DIMENSION 301 THE DIMENSION OF A WIGGLY LINE 307 FIELD EXAMPLES 309 RULERS AND BOXES 313 SUMMARY 314 22 CAPACITY AND HAUSDORFF DIMENSION 315 CAPACITY 315 HAUSDORFF DIMENSION 316 SUMMARY 320 23 INFORMATION DIMENSION 321 DEVELOPMENT 322 A SIMPLIFIED EXAMPLE 326 SUMMARY 327 24 CORRELATION DIMENSION 329 MEASURING PROCEDURE 329 DEFINING THE CORRELATION DIMENSION 334 DETERMINISTIC AND RANDOM CORRELATION DIMENSIONS 338 SUMMARY OF COMPUTATION PROCEDURE 339 PRACTICAL CONSIDERATIONS AND PROBLEMS 340 SUMMARY 348 PART VII QUANTITATIVE MEASURES OF CHAOS 351 2 5 LYAPUNOV EXPONENTS 353 LOCAL CONVERGENCE OR DIVERGENCE OF NEIGHBORING TRAJECTORIES 354 VARIABILITY OF LOCAL CONVERGENCE AND DIVERGENCE RATES OVER THE ATTRACTOR 362 LOCAL LYAPUNOV EXPONENTS 362 DEFINITION OF LYAPUNOV EXPONENT 363 LYAPUNOV SPECTRUM 371 IX CONTENTS PRACTICAL CALCULATION OF LYAPUNOV EXPONENTS 375 SUMMARY 380 26 KOLMOGOROV-SINAI ENTROPY 381 SELECTED MILESTONES IN THE HISTORY OF ENTROPY 381 INTERPRETATIONS OF ENTROPY 384 KOLMOGOROV-SINAI ENTROPY DEFINED 390 ESTIMATING K-S ENTROPY 394 SOME FEATURES THAT INFLUENCE COMPUTED VALUES OF ENTROPY 395 IDENTIFYING THE DYNAMICAL REGIME 398 SUMMARY 404 27 MUTUAL INFORMATION AND REDUNDANCY 407 JOINT AND CONDITIONAL ENTROPIES 408 MUTUAL INFORMATION 417 REDUNDANCY 424 SUMMARY 441 EPILOGUE 443 APPENDIX SELECTED LAWS OF POWERS, ROOTS AND LOGARITHMS 445 GLOSSARY 447 REFERENCES 47 1 SELECTED FURTHER READING 483 INDEX 485
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spelling	Williams, Garnett P. Verfasser aut Chaos theory tamed Garnett P. Williams London Taylor & Francis 1997 XVII, 499 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chaos (théorie des systèmes) ram Chaos gtt Dynamische systemen gtt Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd rswk-swf Chaostheorie (DE-588)4009754-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007840053&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Williams, Garnett P. Chaos theory tamed Chaos (théorie des systèmes) ram Chaos gtt Dynamische systemen gtt Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd
subject_GND	(DE-588)4009754-7
title	Chaos theory tamed
title_auth	Chaos theory tamed
title_exact_search	Chaos theory tamed
title_full	Chaos theory tamed Garnett P. Williams
title_fullStr	Chaos theory tamed Garnett P. Williams
title_full_unstemmed	Chaos theory tamed Garnett P. Williams
title_short	Chaos theory tamed
title_sort	chaos theory tamed
topic	Chaos (théorie des systèmes) ram Chaos gtt Dynamische systemen gtt Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd
topic_facet	Chaos (théorie des systèmes) Chaos Dynamische systemen Chaotic behavior in systems Chaostheorie
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