Global numerical analysis of uncertain dynamical systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Düsseldorf
VDI-Verl.
2010
|
| Edition: | Als Ms. gedr. |
| Series: | Fortschritt-Berichte VDI
Reihe 18, Mechanik/Bruchmechanik ; 327 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 179 S. Ill., graph. Darst. 21 cm |
| ISBN: | 9783183327188 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
CONTENTS
NOMENCLATURE VII
1. INTRODUCTION 1
1.1. OVERVIEW AND MOTIVATION 1
1.2. STATE OF RESEARCH 2
1.2.1. UNCERTAIN DYNAMICAL SYSTEMS 2
1.2.2. GLOBAL NUMERICAL ANALYSIS OF DYNAMICAL SYSTEMS 3 1.3. CONTENTS
AND STRUCTURE OF THE THESIS 4
2. DETERMINISTIC DYNAMICAL SYSTEMS 7
2.1. DEFINITION OF DYNAMICAL SYSTEMS 7
2.2. GENERATION OF DETERMINISTIC SYSTEMS 9
2.3. MARKOV REPRESENTATION OF DYNAMICAL SYSTEMS 11
2.3.1. MOTIVATION 11
2.3.2. DYNAMICAL SYSTEMS AND TRANSITION OPERATORS 14
3. UNCERTAIN DYNAMICAL SYSTEMS 18
3.1. INTRODUCTION 18
3.2. MATHEMATICAL MODEL 20
3.2.1. GENERAL SET-UP 21
3.2.2. MARKOVIAN DYNAMICAL SYSTEMS 25
3.2.3. NONSINGULAR MARKOV SYSTEMS 29
3.3. DISCRETE-TIME MARKOV SYSTEMS 32
3.3.1. TIME DISCRETIZATION 32
3.3.2. REGULARIZATION 33
3.3.3. CONVERGENCE PROPERTIES 39
3.4. CHARACTERIZATION OF MARKOVIAN DYNAMICAL SYSTEMS 45
3.4.1. FELLER PROPERTY 45
3.4.2. DYNAMICAL INVARIANTS 49
3.4.3. ERGODIC DECOMPOSITION 53
3.5. RECAPITULATION 61
4. NUMERICAL ANALYSIS 63
4.1. SPATIAL DISCRETIZATION OF MARKOVIAN DYNAMICAL SYSTEMS 63 4.2.
SUPPLEMENTS 69
4.2.1. SINK CELL 70
4.2.2. CELL SPACE PROJECTION 70
4.3. NUMERICAL APPROXIMATION OF THE CELL MAPPING SYSTEM 71
4.3.1. MONTE CARLO METHODS 72
4.3.2. EXHAUSTION TECHNIQUES 75
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009690485
DIGITALISIERT DURCH
IMAGE 2
VI CONTENTS
4.4. ANALYSIS OF CELL MAPPING SYSTEMS 88
4.4.1. ERGODIC DECOMPOSITION 89
4.4.2. IDENTIFICATION OF ERGODIC SETS 94
4.4.3. IDENTIFICATION OF STABLE AND MULTISTABLE SETS 99
4.5. CELL SPACE REFINEMENT 100
4.5.1. MOTIVATION 100
4.5.2. UNIFORM REFINEMENT 103
4.5.3. ADAPTIVE REFINEMENT 104
4.6. RECAPITULATION 113
5. APPLICATIONS 115
5.1. PRELIMINARY REMARKS 115
5.2. OSCILLATOR CHAIN 116
5.3. THREE-WELL POTENTIAL OSCILLATOR 122
5.3.1. DESCRIPTION OF THE MODEL 122
5.3.2. PERIODICALLY FORCED SYSTEM 124
5.3.3. RANDOMLY FORCED SYSTEM 127
5.4. SHIP IN RANDOM SEA 132
6. CONCLUSIONS 137
6.1. SUMMARY 137
6.2. CONTRIBUTIONS 139
A. LEMMATA AND PROOFS 141
A.L. AUXILIARY LEMMATA 141
A.2. PROOF OF LEMMA 3.7 143
A.3. PROOF OF THEOREM 3.33 145
A.4. PROOF OF THEOREM 4.26 146
B. MATHEMATICAL PRELIMINARIES 152
B.I. GENERAL NOTATIONS 152
B.2. MEASURE THEORY 154
B.3. INTEGRATION THEORY 158
B.4. PROBABILITY THEORY 161
B.5. STOCHASTIC PROCESSES 166
B.6. GRAPH THEORY 168
BIBLIOGRAPHY 169
|
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| dewey-full | 518.28 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.28 |
| dewey-search | 518.28 |
| dewey-sort | 3518.28 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | Als Ms. gedr. |
| format | Thesis Book |
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| id | DE-604.BV036885849 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:50:11Z |
| institution | BVB |
| isbn | 9783183327188 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020801129 |
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| physical | IX, 179 S. Ill., graph. Darst. 21 cm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | VDI-Verl. |
| record_format | marc |
| series | Fortschritt-Berichte VDI |
| series2 | Fortschritt-Berichte VDI : Reihe 18, Mechanik/Bruchmechanik |
| spelling | Gaull, Andreas 1979- Verfasser (DE-588)1063746434 aut Global numerical analysis of uncertain dynamical systems Andreas Gaull Als Ms. gedr. Düsseldorf VDI-Verl. 2010 IX, 179 S. Ill., graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Fortschritt-Berichte VDI : Reihe 18, Mechanik/Bruchmechanik 327 Zugl.: Hamburg-Harburg, Techn. Univ., Diss., 2010 Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Nichtlineares dynamisches System (DE-588)4126142-2 s Stochastische Differentialgleichung (DE-588)4057621-8 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Fortschritt-Berichte VDI Reihe 18, Mechanik/Bruchmechanik ; 327 (DE-604)BV001902156 327 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020801129&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gaull, Andreas 1979- Global numerical analysis of uncertain dynamical systems Fortschritt-Berichte VDI Stochastische Differentialgleichung (DE-588)4057621-8 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4126142-2 (DE-588)4128130-5 (DE-588)4113937-9 |
| title | Global numerical analysis of uncertain dynamical systems |
| title_auth | Global numerical analysis of uncertain dynamical systems |
| title_exact_search | Global numerical analysis of uncertain dynamical systems |
| title_full | Global numerical analysis of uncertain dynamical systems Andreas Gaull |
| title_fullStr | Global numerical analysis of uncertain dynamical systems Andreas Gaull |
| title_full_unstemmed | Global numerical analysis of uncertain dynamical systems Andreas Gaull |
| title_short | Global numerical analysis of uncertain dynamical systems |
| title_sort | global numerical analysis of uncertain dynamical systems |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Stochastische Differentialgleichung Nichtlineares dynamisches System Numerisches Verfahren Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020801129&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001902156 |
| work_keys_str_mv | AT gaullandreas globalnumericalanalysisofuncertaindynamicalsystems |