Non-linear dynamics in geophysics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Chichester [u.a.]
Wiley [u.a.]
1998
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| Series: | Wiley-Praxis series in geophysics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 261 S. Ill., graph. Darst. |
| ISBN: | 0471978531 |
Staff View
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Record in the Search Index
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| adam_text | NON-LINEAR DYNAMICS IN GEOPHYSICS JACQUES DUBOIS PROFESSOR OF
GEOPHYSICS, PARIS UNIVERSITY, FRANCE JOHN WILEY & SONS CHICHESTER * NEW
YORK * WEINHEIM * BRISBANE * SINGAPORE * TORONTO / PUBLISHED IN
ASSOCIATION WITH PRAXIS PRAXIS PUBLISHING TABLE OF CONTENTS INTRODUCTION
1 1 NATURAL PHENOMENA AND NON-LINEAR DYNAMICS 1 2 OUTLINE OF THIS WORK 3
1. FRACTAL AND MULTIFRACTAL THEORY 9 1.1 NOTION OF MEASURE 9 1.1.1
MEASURING BY COUNTING 10 1.1.2 MASS OF A POINT 10 1.1.3 LEBESGUE MEASURE
IN 3$ AND ^ * 10 1.1.4 HAUSDORFF MEASURE 11 1.2 NOTION OF DIMENSION
13 1.2.1 HAUSDORFF DIMENSION 13 1.2.2 ANOTHER DEFINITION OF THE
HAUSDORFF DIMENSION 15 1.3 FRACTAL SETS 17 1.3.1 DEFINITIONS 17 1.3.2
TRIADIC CANTOR SET 18 1.3.3 DIMENSION OF THE TRIADIC CANTOR SET 20 1.3.4
SOME CHARACTERISTIC PROPERTIES OF THE TRIADIC CANTOR SET 21 1.3.5 RANDOM
CANTOR SET 21 1.3.6 OTHER EXAMPLES OF FRACTAL SETS 23 1.3.7 COMPUTATION
OF THE FRACTAL DIMENSION 25 1.3.8 A FEW PROPERTIES OF FRACTAL SETS:
PROJECTION, PRODUCT, INTERSECTION 27 1.4 DYNAMIC SYSTEMS 31 1.4.1 THE
HARMONIC OSCILLATOR 31 1.4.2 THE SIMPLE PENDULUM 32 1.4.3 COUPLED
HARMONIC OSCILLATORS 33 VI TABLE OF CONTENTS 1.4.4 SYSTEMS WITH CENTRAL
AND NON-CENTRAL FORCE FIELDS 34 1.4.5 SUMMARY 37 1.5 LIMIT CYCLES AND
ATTRACTORS 37 1.5.1 THE ATTRACTION PROCESS 37 1.5.2 AREA CONTRACTION 38
1.5.3 APERIODIC ATTRACTORS, CHAOTIC REGIME, STRANGE ATTRACTORS 39 1.5.4
PRACTICAL SEARCH FOR AN ATTRACTOR AND ITS DIMENSION 41 1.5.5 EXAMPLES OF
STRANGE ATTRACTORS 44 1.5.6 LYAPUNOV EXPONENTS 49 1.5.7 POINCARE
SECTIONS AND FIRST-RETURN MAPS 53 1.5.8 LOGISTIC MAP, SUB-HARMONIC
CASCADE AND CHAOS 55 1.6 MULTIFRACTALS AND WAVELET TRANSFORMS 59 1.6.1
NOTION OF GENERALISED DIMENSION 59 1.6.2 MULTIFRACTALS - THEORY AND
PRACTICE 62 1.6.3 WAVELET TRANSFORM 67 1.7 NOTION OF CHAOS 71 1.7.1 THE
PATH TO CHAOS - HOPF BIFURCATION 71 1.7.2 FROM THE T 2 TOROID TO THE
TOROID - THEORY OF RUELLE-TAKENS 76 1.7.3 THE CURRY AND YORKE MODEL 77
1.7.4 DEFINITIONS OF CHAOS 80 2. APPLICATIONS TO GEOPHYSICS 81 2.1
GEOMORPHOLOGY 82 2.1.1 OBSERVATIONS 82 2.1.2 FRACTAL SELF-AFFINE
TOPOGRAPHIC PROFILES 83 2.1.3 2-D REPRESENTATION 85 2.2 FRAGMENTATION,
FRACTURATION, TECTONICS, PERCOLATION 87 2.2.1 FRAGMENTATION 87 2.2.2
ROCK FRACTURATION 95 2.2.3 TECTONICS - STUDY OF SURFACE FAULTS 101 2.2.4
PERCOLATION 103 2.3 SEISMICITY - GUTENBERG-RICHTER LAW 107 2.3.1 POWER
LAW OR POISSON LAW ? 107 2.4 FRAGMENTATION - TECTONICS - SEISMICITY 113
2.5 PROBABILISTIC APPROACH - APPLICATIONS 116 2.5.1 OBSERVABLES 116
2.5.2 APPLICATION TO VOLCANIC ERUPTIONS 118 2.5.3 CANTOR DUST 119 2.5.4
CORRELATION FUNCTION 120 2.5.5 FIRST-RETURN MAP 122 2.5.6 MULTIFRACTAL
ANALYSES 124 2.6 SELF-ORGANISED CRITICALITY: SOC 126 2.7 THE RUSSIAN
METHOD: ALGORITHMS M8 AND CN 129 2.7.1 PRINCIPLES 130 2.7.2 THE M8
ALGORITHM 130 2.7.3 THE CN ALGORITHM 133 2.8 GEOMAGNETISM 137 2.8.1
INVERSIONS OF THE EARTH S MAGNETIC FIELD 137 2.8.2 TEMPORAL VARIATIONS
OF THE MAGNETIC FIELD VECTOR 143 TABLE OF CONTENTS VII 3. PERSPECTIVES
149 3.1 GENERAL POINTS 149 3.2 CHAOTIC TIME SERIES 151 3.3 FRACTALS,
MULTIFRACTALS AND WAVELET TRANSFORMS 154 3.4 SELF-ORGANISED CRITICALITY
(SOC) 154 3.5 THE PROBLEM OF SHORT SERIES 156 3.6 MASTERING AND
CONTROLLING CHAOS 157 4. ILLUSTRATIONS OF NON-LINEAR DYNAMICS 159 4.1
FRACTAL SETS 159 4.1.1 THE OLBERS PARADOX 160 4.1.2 ITERATED FUNCTION
SYSTEMS (IFS) 160 4.1.3 JULIA SET-MANDELBROT SET 165 4.2 DYNAMIC SYSTEMS
169 4.2.1 SINAI S BILLIARDS 169 4.2.2 THE BAKER TRANSFORM 169 4.3
SELF-ORGANISED CRITICALITY 171 4.3.1 THE GAME OF LIFE 171 ANNEX A -
FRACTAL THEORY 173 A.I MEASURE THEORY 173 A. 1.1 DEFINITION OF THE
HAUSDORFF MEASURE 173 A. 1.2 ABOUT THE NOTIONS OF MEASURE AND DIMENSION
174 A. 1.3 ABOUT THE HAUSDORFF DIMENSION 175 A.2 FRACTALS 175 A.2.1
HOLDER FUNCTION, HOLDER CONDITION, LIPSCHITZ MAP 175 A.2.2 MANDELBROT
SET ON QUATERNIONS 177 A.2.3 FRACTAL PROJECTIONS 178 A.3 DYNAMIC SYSTEMS
AND CHAOS 181 A.3.1 DEGREE OF FREEDOM, PHASE SPACE, PHASE TRAJECTORIES
182 A.3.2 CHAOS APPLIED TO DYNAMIC SYSTEMS 182 A.3.3 CONTROL OF CHAOTIC
SYSTEMS 183 A.4 MULTIFRACTALS 188 A.4.1 THE HISTOGRAM METHOD 18 8 A.4.2
THE MOMENTS METHOD 189 ANNEX B - APPLICATIONS TO GEOPHYSICS 195 B.I
GEOMORPHOLOGY 19 5 B. 1.1 FRACTAL ANALYSIS OF RIVER NETWORKS 195 B.1.2
SCALE INVARIANCE AND GEOID ROUGHNESS 198 B.2 FRAGMENTATION,
FRACTURATION, TECTONICS AND PERCOLATION 203 B.2.1 FRACTURATION AND AN
ANISOTROPIC MODEL 203 B.2.2 PERCOLATION, A GEOMETRIC DISORDER 210 B.3
SEISMOLOGY - RUSSIAN METHODS 219 VIII TABLE OF CONTENTS B. 3.1
PREDICTION METHOD OF P. SHEBALIN AND I. ROTWAIN 219 B.4 GEOMAGNETISM 224
B.4.1 STUDY OF A LONG MAGNETIC SERIES 224 B.5 PALAEONTOLOGICAL STUDIES
OF EVOLUTION 232 BIBLIOGRAPHY 235 INDEX 253 THE COLOUR PLATE SECTION IS
BETWEEN PAGES 192 AND 193
|
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| isbn | 0471978531 |
| language | English French |
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| physical | XXII, 261 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Wiley [u.a.] |
| record_format | marc |
| series2 | Wiley-Praxis series in geophysics |
| spelling | Dubois, Jacques Verfasser aut La dynamique non linéaire en physique du globe Non-linear dynamics in geophysics Jacques Dubois Chichester [u.a.] Wiley [u.a.] 1998 XXII, 261 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-Praxis series in geophysics Géodynamique ram Géophysique ram Théories non-linéaires ram Geodynamics Geophysics Nonlinear theories Geophysik (DE-588)4020252-5 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Geophysik (DE-588)4020252-5 s Nichtlineare Dynamik (DE-588)4126141-0 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008269400&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dubois, Jacques Non-linear dynamics in geophysics Géodynamique ram Géophysique ram Théories non-linéaires ram Geodynamics Geophysics Nonlinear theories Geophysik (DE-588)4020252-5 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| subject_GND | (DE-588)4020252-5 (DE-588)4126141-0 |
| title | Non-linear dynamics in geophysics |
| title_alt | La dynamique non linéaire en physique du globe |
| title_auth | Non-linear dynamics in geophysics |
| title_exact_search | Non-linear dynamics in geophysics |
| title_full | Non-linear dynamics in geophysics Jacques Dubois |
| title_fullStr | Non-linear dynamics in geophysics Jacques Dubois |
| title_full_unstemmed | Non-linear dynamics in geophysics Jacques Dubois |
| title_short | Non-linear dynamics in geophysics |
| title_sort | non linear dynamics in geophysics |
| topic | Géodynamique ram Géophysique ram Théories non-linéaires ram Geodynamics Geophysics Nonlinear theories Geophysik (DE-588)4020252-5 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| topic_facet | Géodynamique Géophysique Théories non-linéaires Geodynamics Geophysics Nonlinear theories Geophysik Nichtlineare Dynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008269400&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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