Hamiltonian chaos beyond the KAM theory: dedicated to George M. Zaslavsky (1935-2008)
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Beijing
Higher Education Press
2010
|
| Schriftenreihe: | Nonlinear physical science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XVIII, 292 S. Ill., graph. Darst. |
| ISBN: | 9787040291872 9783642127175 |
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
1 STOCHASTIC AND RESONANT LAYERS IN NONLINEAR HAMILTONIAN SYSTEMS ALBERT
C.J. LUO 1
1.1 INTRODUCTION 1
1.2 STOCHASTIC LAYERS 4
1.2.1 GEOMETRICAL DESCRIPTION 5
1.2.2 APPROXIMATE ENTERIONS 9
1.3 RESONANT LAYERS 17
1.3.1 LAYER DYNAMICS 19
1.3.2 APPROXIMATE CRITERIONS 23
1.4 A PERIODICALLY FORCED DUFFING OSCILLATOR 27
1.4.1 APPROXIMATE PREDICTIONS 28
1.4.2 NUMERICAL ILLUSTRATIONS 34
1.5 DISCUSSIONS 47
REFERENCES 48
2 A NEW APPROACH TO THE TREATMENT OF SEPARATRIX CHAOS AND ITS
APPLICATIONS S.M. SOSKIN, R. MANNELLA, O.M. YEVTUSHENKO, I.A. KHOVANOV,
P.V.E. MCCLINTOCK 51
2.1 INTRODUCTION 52
2.1.1 HEURISTIC RESULTS 52
2.1.2 MATHEMATICAL AND ACCURATE PHYSICAL RESULTS 53
2.1.3 NUMERICAL EVIDENCE FOR HIGH PEAKS IN AE((OF) AND THEIR ROUGH
ESTIMATIONS 54
2.1.4 ACCURATE DESCRIPTION OF THE PEAKS AND OF THE RELATED PHENOMENA 54
2.2 BASIC IDEAS OF THE APPROACH 55
2.3 SINGLE-SEPARATRIX CHAOTIC LAYER 60
2.3.1 ROUGH ESTIMATES. CLASSIFICATION OF SYSTEMS 61
2.3.2 ASYMPTOTIC THEORY FOR SYSTEMS OF TYPE 1 62
2.3.3 ASYMPTOTIC THEORY FOR SYSTEMS OF TYPE II 71
2.3.4 ESTIMATE OF THE NEXT-ORDER CORRECTIONS 79
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1002586763
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
2.3.5 DISCUSSION 83
2.4 DOUBLE-SEPARATRIX CHAOS 85
2.4.1 ASYMPTOTIC THEORY FOR THE MINIMA OF THE SPIKES 89 2.4.2 THEORY OF
THE SPIKES'WINGS 108
2.4.3 GENERALIZATIONS AND APPLICATIONS 114
2.5 EMARGEMENT OF A LOW-DIMENSIONAL STOCHASTIC WEB 117
2.5.1 SLOW MODULATION OF THE WAVE ANGLE 119
2.5.2 APPLICATION TO SEMICONDUCTOR SUPERLATTICES 120
2.5.3 DISCUSSION 121
2.6 CONCLUSIONS 121
2.7 APPENDIX 122
2.7.1 LOWER CHAOTIC LAYER 122
2.7.2 UPPER CHAOTIC LAYER 137
REFERENCES 138
HAMILTONIAN CHAOS AND ANOMALOUS TRANSPORT IN TWO DIMENSIONAL FIOWS
XAVIER LEONCINI 143
3.1 INTRODUCTION 143
3.2 POINT VORTICES AND PASSIVE TRACERS ADVECTION 145
3.2.1 DEFINITIONS 145
3.2.2 CHAOTIC ADVECTION 146
3.3 A SYSTEM OF POINT VORTICES 148
3.3.1 DEFINITIONS 148
3.4 DYNAMICS OF SYSTEMS WITH TWO OR THREE POINT VORTICES 150 3.4.1
DYNAMICS OF TWO VORTICES 150
3.4.2 DYNAMICS OF THREE VORTICES 151
3.5 VBRTEX COLLAPSE AND NEAR COLLAPSE DYNAMICS OF POINT VORTICES 152
3.5.1 VBRTEX COLLAPSE 153
3.5.2 VBRTEX DYNAMICS IN THE VICINITY OF THE SINGULARITY 153 3.6 CHAOTIC
ADVECTION AND ANOMALOUS TRANSPORT 155
3.6.1 ABRIEFHISTORY 156
3.6.2 DEFINITIONS 157
3.6.3 ANOMALOUS TRANSPORT IN INCOMPRESSIBLE FLOWS 160 3.6.4 TRACERS
(PASSIVE PARTICLES) DYNAMICS 162
3.6.5 TRANSPORT PROPERTIES 169
3.6.6 ORIGIN OF ANOMALOUS TRANSPORT 174
3.6.7 GENERAL REMARKS 180
3.7 BEYOND CHARACTERIZING TRANSPORT 180
3.7.1 CHAOS OFFIELD LINES 180
3.7.2 LOCAL HAMILTONIAN DYNAMICS 180
3.7.3 AN ABC TYPE FLOW 182
3.8 TARGETED MIXING IN AN ARRAY OF ALTERNATING VORTICES 185
3.9 CONCLUSION 189
REFERENCES 189
IMAGE 3
CONTENTS
HAMILTONIAN CHAOS WITH A COLD ATOM IN AN OPTICAL LATTICE S.V.PRANTS 193
4.1 SHORT HISTORICAL BACKGROUND 194
4.2 INTRODUCTION 195
4.3 SEMICLASSICAL DYNAMICS 196
4.3.1 HAMILTON-SCHROEDINGER EQUATIONS OF MOTION 196 4.3.2 REGIMES OF
MOTION 198
4.3.3 STOCHASTIC MAP FOR CHAOTIC ATOMIC TRANSPORT 200
4.3.4 STATISTICAL PROPERTIES OF CHAOTIC TRANSPORT 202
4.3.5 DYNAMICAL FRACTALS 204
4.4 QUANTUM DYNAMICS 208
4.5 DRESSED STATES PICTURE AND NONADIABATIC TRANSITIONS 209 4.5.1 WAVE
PACKET MOTION IN THE MOMENTUM SPACE 211 4.6 QUANTUM-CLASSICAL
CORRESPONDENCE AND MANIFESTATIONS OF DYNAMICAL CHAOS IN WAVE-PACKET
ATOMIC MOTION 219
REFERENCES 221
USING STOCHASTIC WEBS TO CONTROL THE QUANTUM TRANSPORT OF ELECTRONS IN
SEMICONDUCTOR SUPERLATTICES T.M. FROMHOLD, A.A. KROKHIN, S. BUJKIEWICZ,
P.B. WILKINSON, D. FOWLER, A. PATANE, L. EAVES, D.P.A. HARDWICK, A.G.
BALANOV,
M. T. GREENAWAY, A. HENNING 225
5.1 INTRODUCTION 226
5.2 SUPERLATTICE STRUCTURES 228
5.3 SEMICLASSICAL ELECTRON DYNAMICS 231
5.4 ELECTRON DRIFT VELOCITY 234
5.5 CURRENT-VOLTAGE CHARACTERISTICS: THEORY AND EXPERIMENT 236 5.6
ELECTROSTATICS AND CHARGE DOMAIN STRUCTURE 238
5.7 TAILORING THE SL STRUCTURE TO INCREASE THE NUMBER OF CONDUCTANCE
RESONANCES 240
5.8 ENERGY EIGENSTATES AND WIGNER FUNCTIONS 243
5.9 SUMMARY AND OUTLOOK 247
REFERENCES 249
CHAOS IN OCEAN ACOUSTIC WAVEGUIDE A.L. VIROVLYANSKY 255
6.1 INTRODUCTION 255
6.2 BASIC EQUATIONS 258
6.2.1 PARABOLIC EQUATION APPROXIMATION 259
6.2.2 GEOMETRICAL OPTICS. HAMILTONIAN FORMALISM 260 6.2.3 MODAL
REPRESENTATION OF THE WAVE FIELD 262
6.2.4 RAY-BASED DESCRIPTION OF NORMAL MODES 263
6.3 RAY CHAOS 264
6.3.1 STATISTICAL DESCRIPTION OF CHAOTIC RAYS 264
6.3.2 ENVIRONMENTAL MODEL 266
IMAGE 4
CONTENTS
6.3.3 WIENER PROCESS APPROXIMATION 267
6.3.4 DISTRIBUTION OF RAY PARAMETERS 269
6.3.5 SMOOTHED INTENSITY OF THE WAVE FIELD 270
6.4 RAY TRAVEL TIMES 272
6.4.1 TIMEFRONT 272
6.4.2 STATISTICS OF RAY TRAVEL TIMES 274
6.5 MODAL STRUCTURE OF THE WAVE FIELD UNDER CONDITIONS OF RAY CHAOS . .
278 6.5.1 COARSE-GRAINED ENERGY DISTRIBUTION BETWEEN NORMAL MODES. 278
6.5.2 TRANSIENT WAVE FIELD 280
6.6 CONCLUSION 287
REFERENCES 289 |
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| spelling | Hamiltonian chaos beyond the KAM theory dedicated to George M. Zaslavsky (1935-2008) Albert C. J. Luo ; Valentin Afraimovich Beijing Higher Education Press 2010 XVIII, 292 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonlinear physical science Literaturangaben Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf KAM-Theorie (DE-588)4329269-0 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Hamiltonsches System (DE-588)4139943-2 s Nichtlineare Dynamik (DE-588)4126141-0 s Chaostheorie (DE-588)4009754-7 s KAM-Theorie (DE-588)4329269-0 s DE-604 Luo, Albert C. J. 1964- Sonstige (DE-588)142378097 oth X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3478437&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021095843&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hamiltonian chaos beyond the KAM theory dedicated to George M. Zaslavsky (1935-2008) Nichtlineare Dynamik (DE-588)4126141-0 gnd Hamiltonsches System (DE-588)4139943-2 gnd Chaostheorie (DE-588)4009754-7 gnd KAM-Theorie (DE-588)4329269-0 gnd |
| subject_GND | (DE-588)4126141-0 (DE-588)4139943-2 (DE-588)4009754-7 (DE-588)4329269-0 (DE-588)4143413-4 |
| title | Hamiltonian chaos beyond the KAM theory dedicated to George M. Zaslavsky (1935-2008) |
| title_auth | Hamiltonian chaos beyond the KAM theory dedicated to George M. Zaslavsky (1935-2008) |
| title_exact_search | Hamiltonian chaos beyond the KAM theory dedicated to George M. Zaslavsky (1935-2008) |
| title_full | Hamiltonian chaos beyond the KAM theory dedicated to George M. Zaslavsky (1935-2008) Albert C. J. Luo ; Valentin Afraimovich |
| title_fullStr | Hamiltonian chaos beyond the KAM theory dedicated to George M. Zaslavsky (1935-2008) Albert C. J. Luo ; Valentin Afraimovich |
| title_full_unstemmed | Hamiltonian chaos beyond the KAM theory dedicated to George M. Zaslavsky (1935-2008) Albert C. J. Luo ; Valentin Afraimovich |
| title_short | Hamiltonian chaos beyond the KAM theory |
| title_sort | hamiltonian chaos beyond the kam theory dedicated to george m zaslavsky 1935 2008 |
| title_sub | dedicated to George M. Zaslavsky (1935-2008) |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd Hamiltonsches System (DE-588)4139943-2 gnd Chaostheorie (DE-588)4009754-7 gnd KAM-Theorie (DE-588)4329269-0 gnd |
| topic_facet | Nichtlineare Dynamik Hamiltonsches System Chaostheorie KAM-Theorie Aufsatzsammlung |
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