Multifractals: theory and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 248 S. Ill., graph. Darst. |
| ISBN: | 1584881542 |
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Record in the Search Index
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| adam_text | M MILL THEORY AND APPLICATIONS DAVID HARTE CHAPMAN & HALL/CRC BOCA RATON
LONDON NEW YORK WASHINGTON, D.C. CONTENTS PREFACE V LIST OF FIGURES VII
LIST OF NOTATION IX I INTRODUCTION AND PRELIMINARIES 1 1 MOTIVATION AND
BACKGROUND 3 1.1 INTRODUCTION 3 1.2 FRACTAL SETS AND MULTIFRACTAL
MEASURES 3 1.3 DYNAMICAL SYSTEMS 8 1.4 TURBULENCE 14 1.5 RAINFALL FIELDS
16 1.6 EARTHQUAKE MODELLING 17 1.7 OTHER APPLICATIONS 22 1.8 CONCEPT OF
MULTIFRACTALS 22 1.9 OVERVIEW OF BOOK 25 2 THE MULTIFRACTAL FORMALISM 29
2.1 INTRODUCTION 29 2.2 HISTORICAL DEVELOPMENT OF GENERALISED RENYI
DIMENSIONS 30 2.3 GENERALISED RE NYI LATTICE DIMENSIONS 33 2.4
GENERALISED RENYI POINT CENTRED DIMENSIONS 35 2.5 MULTIFRACTAL SPECTRUM
AND FORMALISM 38 2.6 REVIEW OF RELATED LATTICE BASED RESULTS 41 2.7
REVIEW OF RELATED POINT CENTRED RESULTS 43 3 THE MULTINOMIAL MEASURE 47
3.1 INTRODUCTION 47 3.2 LOCAL BEHAVIOUR 48 3.3 GLOBAL AVERAGING AND
LEGENDRE TRANSFORMS 50 3.4 FRACTAL DIMENSIONS 54 3.5 POINT CENTRED
CONSTRUCTION 56 XII CONTENTS N MULTIFRACTAL FORMALISM USING LARGE
DEVIATIONS 59 4 LATTICE BASED MULTIFRACTALS 61 4.1 INTRODUCTION 61 4.2
LARGE DEVIATION FORMALISM 62 4.3 UNIFORM SPATIAL SAMPLING MEASURE 65 4.4
A FAMILY OF SAMPLING MEASURES 69 4.5 HAUSDORFF DIMENSIONS 72 5 POINT
CENTRED MULTIFRACTALS 77 5.1 INTRODUCTION 77 5.2 LARGE DEVIATION
FORMALISM 77 5.3 A FAMILY OF SAMPLING MEASURES 79 5.4 HAUSDORFF
DIMENSIONS 81 5.5 RELATIONSHIPS BETWEEN LATTICE AND POINT CENTRED
CONSTRUCTIONS 83 6 MULTIPLICATIVE CASCADE PROCESSES 89 6.1 INTRODUCTION
89 6.2 MORAN CASCADE PROCESSES 94 6.3 RANDOM CASCADES 99 6.4 OTHER
CASCADE PROCESSES 109 III ESTIMATION OF THE RENYI DIMENSIONS 111 7
INTERPOINT DISTANCES OF ORDER Q AND INTRINSIC BIAS 113 7.1 INTRODUCTION
TO PART IN 113 7.2 BOUNDARY EFFECT 116 7.3 MULTIPLICITY OF BOUNDARIES
120 7.4 DECOMPOSITION OF FY (Y) 122 7.5 DIFFERENTIABLE DISTRIBUTIONS 126
8 ESTIMATION OF POINT CENTRED RENYI DIMENSIONS WITH G 2 127 8.1
INTRODUCTION 127 8.2 GENERALISED GRASSBERGER-PROCACCIA ALGORITHM 129 8.3
TAKENS ESTIMATOR 131 8.4 HILL ESTIMATOR 133 8.5 BOOTSTRAP ESTIMATION
PROCEDURE 140 8.6 DISCUSSION AND EXAMPLES 144 9 EXTRINSIC SOURCES OF
BIAS 155 9.1 INTRODUCTION 155 9.2 IMPOSED BOUNDARY EFFECT 156 9.3
ROUNDING EFFECT 158 9.4 EFFECT OF NOISE 163 CONTENTS XIII 10
APPLICATIONS OF DIMENSION ESTIMATION 165 10.1 INTRODUCTION 165 10.2 MORE
ON ESTIMATION AND INTERPRETATION 166 10.3 SPATIAL AND TEMPORAL POINT
PATTERNS 170 10.4 DYNAMICAL SYSTEMS 175 10.5 IS A PROCESS STOCHASTIC OR
DETERMINISTIC? 184 10.6 STOCHASTIC PROCESSES WITH POWERLAW PROPERTIES
187 11 EARTHQUAKE ANALYSES 195 11.1 INTRODUCTION 195 11.2 SOURCES OF
DATA 197 11.3 EFFECTS CAUSING BIAS 202 11.4 RESULTS 204 11.5 COMPARISON
OF RESULTS AND CONCLUSIONS 209 IV APPENDICES 215 A PROPERTIES AND
DIMENSIONS OF SETS 217 A.I SELF-SIMILAR SETS 217 A.2 HAUSDORFF DIMENSION
218 A.3 BOX COUNTING DIMENSION 221 A.4 PACKING DIMENSION 223 B LARGE
DEVIATIONS 225 B.I INTRODUCTION 225 B.2 CRAMER S THEOREM 226 B.3
GARTNER-ELLIS THEOREM 229 REFERENCES 235 INDEX 245
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| indexdate | 2024-07-09T18:45:48Z |
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| isbn | 1584881542 |
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| physical | XIII, 248 S. Ill., graph. Darst. |
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| spelling | Harte, David Verfasser aut Multifractals theory and applications David Harte Boca Raton [u.a.] Chapman & Hall/CRC 2001 XIII, 248 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fractals gtt Multifractales Statistiek gtt Waarschijnlijkheidstheorie gtt Statistik Multifractals GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009166715&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harte, David Multifractals theory and applications Fractals gtt Multifractales Statistiek gtt Waarschijnlijkheidstheorie gtt Statistik Multifractals |
| title | Multifractals theory and applications |
| title_auth | Multifractals theory and applications |
| title_exact_search | Multifractals theory and applications |
| title_full | Multifractals theory and applications David Harte |
| title_fullStr | Multifractals theory and applications David Harte |
| title_full_unstemmed | Multifractals theory and applications David Harte |
| title_short | Multifractals |
| title_sort | multifractals theory and applications |
| title_sub | theory and applications |
| topic | Fractals gtt Multifractales Statistiek gtt Waarschijnlijkheidstheorie gtt Statistik Multifractals |
| topic_facet | Fractals Multifractales Statistiek Waarschijnlijkheidstheorie Statistik Multifractals |
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