Pseudochaotic kicked oscillators: renormalization, symbolic dynamics, and transport
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Heidelberg [u.a.]
Springer
2012
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 215 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642281532 3642281532 |
Internformat
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| 100 | 1 | |a Lowenstein, John H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Pseudochaotic kicked oscillators |b renormalization, symbolic dynamics, and transport |c John H. Lowenstein |
| 264 | 1 | |a Heidelberg [u.a.] |b Springer |c 2012 | |
| 300 | |a XII, 215 S. |b graph. Darst. |c 235 mm x 155 mm | ||
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Datensatz im Suchindex
| _version_ | 1804149577158230017 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 KICKED OSCILLATORS 1
1.2 POINCARE SECTIONS 2
1.3 CRYSTALLINE SYMMETRY 3
1.4 STOCHASTIC WEBS 5
1.5 NORMAL AND ANOMALOUS DIFFUSIVE BEHAVIOR 7
1.6 THE SAWTOOTH WEB MAP 9
1.7 RENORMALIZABILITY 10
1.8 LONG-TIME ASYMPTOTICS 12
1.9 LINKING LOCAL AND GLOBAL BEHAVIOR 13
1.10 ORGANIZATION OF THE BOOK 13
REFERENCES 15
2 RENORMALIZABILITY O F THE LOCAL MAP 17
2.1 HEURISTIC APPROACH TO RENORMALIZABILITY 18
2.1.1 GENERALIZED ROTATIONS 18
2.1.2 NATURAL RETURN MAP TREE 19
2.1.3 EXAMPLES 21
2.2 QUADRATIC PIECEWISE ISOMETRIES 26
2.2.1 ARITHMETIC PRELIMINARIES 26
2.2.2 DOMAINS 28
2.2.3 GEOMETRIC TRANSFORMATIONS ON DOMAINS 30
2.2.4 SCALING SEQUENCES 31
2.2.5 PERIODIC ORBITS 33
2.2.6 RECURSIVE TILING 33
2.2.7 COMPUTER-ASSISTED PROOFS 36
2.3 THREE QUADRATIC MODELS 4 0
2.3.1 MODEL I 4 1
2.3.2 MODEL II 43
2.3.3 MODEL III 4 6
HTTP://D-NB.INFO/1018671404
IMAGE 2
X CONTENTS
2.4 PROOF OF RENORMALIZABILITY 4 8
2.5 STRUCTURE OF THE DISCONTINUITY SET 4 9
2.5.1 MODEL I 4 9
2.5.2 MODEL III 50
2.6 MORE GENERAL RENORMALIZATION 51
2.7 THE N / 1 MODEL 53
REFERENCES 61
3 SYMBOLIC DYNAMICS 63
3.1 SYMBOLIC REPRESENTATION OF THE RESIDUAL SET 63
3.1.1 HIERARCHICAL SYMBOL STRINGS 63
3.1.2 EVENTUALLY PERIODIC CODES 65
3.1.3 SIMPLIFIED CODES FOR QUADRATIC MODELS 6 6
3.2 DYNAMICAL UPDATING O F CODES 66
3.3 ADMISSIBILITY 68
3.3.1 QUADRATIC EXAMPLE 70
3.3.2 MODELS I, II, AND III 73
3.3.3 CUBIC EXAMPLE 75
3.4 MINIMALITY 78
REFERENCES 78
4 DIMENSIONS AND MEASURES 79
4.1 HAUSDORFF DIMENSION AND HAUSDORFF MEASURE 79
4.2 CONSTRUCTION OF THE MEASURE 80
4.3 SIMPLIFICATION FOR QUADRATIC IRRATIONAL A 81
4.4 A COMPLICATED EXAMPLE: MODEL II 83
4.5 DISCONTINUITY SET IN MODEL III 84
4.6 MULTIFRACTAL RESIDUAL SET O F THE N / 1 MODEL 85
4.7 ASYMPTOTIC FACTORIZATION 86
4.8 TELESCOPING 91
4.9 UNIQUE ERGODICITY FOR EACH X(I) 9 2
4.10 MULTIFRACTAL SPECTRUM OF RECURRENCE TIME DIMENSIONS 9 4
4.10.1 AUXILIARY MEASURES AND DIMENSIONS 95
4.10.2 SIMPLER CALCULATION O F THE RECURRENCE TIME DIMENSIONS 100 4.10.3
RECURRENCE TIME SPECTRUM FOR THE N / 1 MODEL 102
REFERENCES 105
5 GLOBAL DYNAMICS 107
5.1 GLOBAL EXPANSIVITY 107
5.1.1 LIFTING THE RETURN MAP PFC(0) 107
5.1.2 LIFTING THE HIGHER-LEVEL RETURN MAPS 109
5.2 LONG-TIME ASYMPTOTICS I L L
5.3 QUADRATIC EXAMPLES 114
5.4 CUBIC EXAMPLES 119
5.4.1 ORBITS IN THE (0,K,6) SECTORS 119
IMAGE 3
CONTENTS XI
5.4.2 NUMERICAL INVESTIGATIONS 122
5.4.3 A NON-EXPANSIVE SECTOR 125
5.4.4 GENERIC BEHAVIOR 127
REFERENCES 129
6 TRANSPORT 131
6.1 PROBABILITY CALCULATION USING RECURSIVE TILING 132
6.2 BALLISTIC TRANSPORT IN MODEL I 134
6.3 SUBDIFFUSIVE TRANSPORT IN MODEL II 138
6.4 DIFFUSIVE TRANSPORT IN MODEL II 142
6.5 SUPERDIFFUSIVE TRANSPORT IN MODEL III 143
6.6 DISCUSSION 149
REFERENCES 150
7 HAMILTONIAN ROUND-OFF 151
7.1 VECTOR FIELD 151
7.2 LOCALIZATION 154
7.3 LOCALIZATION O F THE VECTOR FIELD AND PERIODIC ORBITS 155
7.4 SYMBOLIC CODES FOR WALKS 158
7.5 CONSTRUCTION O F THE PROBABILITY DISTRIBUTION 159
7.6 ROTATION NUMBER 1/5 161
7.6.1 RECURSIVE TILING FOR THE LOCAL MAP 161
7.6.2 PROBABILITY DISTRIBUTION P ( X , T ) 163
7.6.3 FRACTAL SNOWFLAKES 165
7.6.4 SUBSTITUTION RULES FOR LATTICE WALKS 168
7.6.5 SEPARATING OUT AN ASYMPTOTIC WALK 170
7.6.6 ASYMPTOTIC SCALING 173
7.7 MODEL I 175
7.8 MODEL II 177
7.9 A CONJECTURE 184
REFERENCES 184
APPENDIX A DATA TABLES 185
A . L MODEL I DATA TABLES, FROM KOUPTSOV ET AL. (2002) 185
A. 1.1 GENERATING DOMAIN 185
A. 1.2 LEVEL-0 SCALING SEQUENCE DOMAINS 185
A. 1.3 LEVEL-0 PERIODIC DOMAINS 186
A. 1.4 MISCELLANEOUS PERIODIC DOMAINS 186
A.2 MODEL II DATA TABLES, FROM KOUPTSOV ET AL. (2002) 186
A.2.1 GENERATING PARTITION 186
A.2.2 LEVEL-0 SCALING DOMAINS, SEQUENCE A 187
A.2.3 LEVEL-0 PERIODIC DOMAINS, SEQUENCE A 188
A.2.4 MISCELLANEOUS PERIODIC DOMAINS, J 10 188
A.2.5 LEVEL-0 SCALING DOMAINS, SEQUENCE B 189
A.2.6 LEVEL-0 PERIODIC DOMAINS, SEQUENCE B 189
IMAGE 4
XII CONTENTS
A.2.7 INCIDENCE MATRICES 190
A.3 MODEL III DATA TABLES, FROM KOUPTSOV ET AL. (2002) 191
A.3.1 GENERATING DOMAIN 191
A.3.2 PRE SCALING LEVEL L = - 1 191
A.3.3 DOMAINS DJ(L) FOR EVEN L 192
A.3.4 DOMAINS DJ(L) FOR ODD L 192
A.3.5 DOMAINS TL^L) FOR ALL L 192
A.3.6 TILING DATA 193
A.3.7 SECTION OF THE DISCONTINUITY SET 193
A.4 CUBIC MODEL DATA TABLES, FROM LOWENSTEIN ET AL. (2004) 194
A.5 INADMISSIBILITY TABLES FOR MODELS II AND III 200
REFERENCES 200
APPENDIX B THE CODOMETER 201
INDEX 205
COLOR FIGURE INDEX 209
|
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| spelling | Lowenstein, John H. Verfasser aut Pseudochaotic kicked oscillators renormalization, symbolic dynamics, and transport John H. Lowenstein Heidelberg [u.a.] Springer 2012 XII, 215 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Symbolische Dynamik (DE-588)4482797-0 gnd rswk-swf Harmonischer Oszillator (DE-588)4159128-8 gnd rswk-swf Renormierung (DE-588)4128419-7 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s Chaotisches System (DE-588)4316104-2 s Harmonischer Oszillator (DE-588)4159128-8 s Renormierung (DE-588)4128419-7 s Symbolische Dynamik (DE-588)4482797-0 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025349612&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lowenstein, John H. Pseudochaotic kicked oscillators renormalization, symbolic dynamics, and transport Symbolische Dynamik (DE-588)4482797-0 gnd Harmonischer Oszillator (DE-588)4159128-8 gnd Renormierung (DE-588)4128419-7 gnd Chaotisches System (DE-588)4316104-2 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| subject_GND | (DE-588)4482797-0 (DE-588)4159128-8 (DE-588)4128419-7 (DE-588)4316104-2 (DE-588)4126141-0 |
| title | Pseudochaotic kicked oscillators renormalization, symbolic dynamics, and transport |
| title_auth | Pseudochaotic kicked oscillators renormalization, symbolic dynamics, and transport |
| title_exact_search | Pseudochaotic kicked oscillators renormalization, symbolic dynamics, and transport |
| title_full | Pseudochaotic kicked oscillators renormalization, symbolic dynamics, and transport John H. Lowenstein |
| title_fullStr | Pseudochaotic kicked oscillators renormalization, symbolic dynamics, and transport John H. Lowenstein |
| title_full_unstemmed | Pseudochaotic kicked oscillators renormalization, symbolic dynamics, and transport John H. Lowenstein |
| title_short | Pseudochaotic kicked oscillators |
| title_sort | pseudochaotic kicked oscillators renormalization symbolic dynamics and transport |
| title_sub | renormalization, symbolic dynamics, and transport |
| topic | Symbolische Dynamik (DE-588)4482797-0 gnd Harmonischer Oszillator (DE-588)4159128-8 gnd Renormierung (DE-588)4128419-7 gnd Chaotisches System (DE-588)4316104-2 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| topic_facet | Symbolische Dynamik Harmonischer Oszillator Renormierung Chaotisches System Nichtlineare Dynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025349612&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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