Complex Hamiltonian dynamics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
|
| Schriftenreihe: | Springer series in synergetics
Springer complexity |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XXIII, 255 S. graph. Darst. 24 cm |
| ISBN: | 9783642273049 9783642273056 3642273041 |
Internformat
MARC
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| 100 | 1 | |a Mpuntēs, Tasos |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Complex Hamiltonian dynamics |c Tassos Bountis ; Haris Skokos |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
| 300 | |a XXIII, 255 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in synergetics | |
| 490 | 0 | |a Springer complexity | |
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| 700 | 1 | |a Skokos, Haris |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804149266057265152 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 PREAMBLE 1
1.2 LYAPUNOV STABILITY O F DYNAMICAL SYSTEMS 3
1.3 HAMILTONIAN DYNAMICAL SYSTEMS 7
1.4 COMPLEX HAMILTONIAN DYNAMICS 10
2 HAMILTONIAN SYSTEMS O F FEW DEGREES O F FREEDOM 13
2.1 T H E CASE O F /V = 1 DEGREE O F FREEDOM 13
2.2 T H E CASE O F /V = 2 DEGREES O F FREEDOM 19
2.2.1 COORDINATE TRANSFORMATIONS AND SOLUTION BY QUADRATURES . . . 2 0
2.2.2 INTEGRABILITY AND SOLVABILITY O F THE EQUATIONS O F MOTION 2 4
2.3 NON-AUTONOMOUS O N E DEGREE O F FREEDOM HAMILTONIAN SYSTEMS . . . .
3 0 2.3.1 T H E DUFFING OSCILLATOR WITH QUADRATIC NONLINEARITY 31
2.3.2 T H E DUFFING OSCILLATOR WITH CUBIC NONLINEARITY 3 4
EXERCISES 3 7
PROBLEMS 39
3 LOCAL AND GLOBAL STABILITY O F MOTION 41
3.1 EQUILIBRIUM POINTS, PERIODIC ORBITS AND LOCAL STABILITY 41
3.1.1 EQUILIBRIUM POINTS 41
3.1.2 PERIODIC ORBITS 4 4
3.2 LINEAR STABILITY ANALYSIS 4 6
3.2.1 AN ANALYTICAL CRITERION FOR WEAK CHAOS 51
3.3 LYAPUNOV CHARACTERISTIC EXPONENTS AND STRONG CHAOS 5 3
3.3.1 LYAPUNOV SPECTRA AND THEIR CONVERGENCE 5 3
3.3.1.1 LYAPUNOV SPECTRA AND THE THERMODYNAMIC LIMIT 5 5
3.4 DISTINGUISHING O R D E R FROM CHAOS 5 6
3.4.1 T H E SAL1 METHOD 5 8
3.4.2 T H E G A L I METHOD 5 9
EXERCISES 6 0
PROBLEMS 61
X V I I
HTTP://D-NB.INFO/1017314721
IMAGE 2
X V I I I
C O N T E N T S
4 NORMAL MODES, SYMMETRIES AND STABILITY 6 3
4.1 NORMAL MODES O F LINEAR ONE-DIMENSIONAL HAMILTONIAN LATTICES . . . 6
3 4.2 NONLINEAR NORMAL MODES (NNMS) AND THE PROBLEM O F CONTINUATION 6 5
4.3 PERIODIC BOUNDARY CONDITIONS AND DISCRETE SYMMETRIES 6 7
4.3.1 N N M S AS ONE-DIMENSIONAL BUSHES 6 7
4.3.2 HIGHER-DIMENSIONAL BUSHES AND QUASIPERIODIC ORBITS 7 0
4.4 A GROUP THEORETICAL STUDY O F BUSHES 7 0
4.4.1 SUBGROUPS O F THE PARENT G R O U P AND BUSHES O F N N M S 7 2
4.4.2 BUSHES IN MODAL SPACE AND STABILITY ANALYSIS 7 4
4.5 APPLICATIONS TO SOLID STATE PHYSICS 8 0
4.5.1 BUSHES O F N N M S FOR A SQUARE MOLECULE 8 0
4.5.2 BUSHES O F N N M S FOR A SIMPLE OCTAHEDRAL MOLECULE 8 4
EXERCISES 87
PROBLEMS 8 8
5 EFFICIENT INDICATORS O F ORDERED AND CHAOTIC MOTION 91
5.1 VARIATIONAL EQUATIONS AND TANGENT M A P 91
5.2 T H E SALI METHOD 9 4
5.3 THE G A L I METHOD 102
5.3.1 THEORETICAL RESULTS FOR THE T I M E EVOLUTION O F G A L I 104
5.3.1.1 EXPONENTIAL DECAY O F G A L I FOR CHAOTIC ORBITS - 104 5.3.1.2 T
H E EVALUATION O F G A L I FOR ORDERED ORBITS 107
5.3.2 NUMERICAL VERIFICATION AND APPLICATIONS 111
5.3.2.1 LOW-DIMENSIONAL HAMILTONIAN SYSTEMS I L L
5.3.2.2 HIGH-DIMENSIONAL HAMILTONIAN SYSTEMS 117
5.3.2.3 SYMPLECTIC MAPS 120
5.3.2.4 MOTION ON LOW-DIMENSIONAL TORI 122
APPENDIX A: WEDGE PRODUCT 124
APPENDIX B: EXAMPLE ALGORITHMS FOR THE COMPUTATION O F THE SALI AND G A
L I CHAOS INDICATORS 126
EXERCISES 130
PROBLEMS 131
6 F P U RECURRENCES AND THE TRANSITION F R O M W E A K TO STRONG CHAOS .
. . . 133 6.1 T H E FERMI PASTA ULAM PROBLEM 133
6.1.1 HISTORICAL REMARKS 133
6.1.2 T H E CONCEPT O F Q-BREATHERS 136
6.1.3 T H E CONCEPT O F Q-TORI 138
6.2 EXISTENCE AND STABILITY O F Q-TORI 139
6.2.1 CONSTRUCTION O F (/-TORI BY POINCARE-LINSTEDT SERIES 140
6.2.2 PROFILE O F THE ENERGY LOCALIZATION 147
6.3 A NUMERICAL STUDY O F FPU TRAJECTORIES 152
6.3.1 LONG TIME STABILITY NEAR Q- TORI 155
IMAGE 3
CONTENTS XIX
6.4 DIFFUSION AND THE BREAKDOWN O F F P U RECURRENCES 157
6.4.1 TWO STAGES O F THE DIFFUSION PROCESS 158
6.4.2 RATE O F DIFFUSION O F ENERGY TO THE TAIL M O D E S 160
6.4.3 TIME INTERVAL FOR ENERGY EQUIPARTITION 162
EXERCISES 163
PROBLEMS 164
7 LOCALIZATION AND DIFFUSION IN NONLINEAR ONE-DIMENSIONAL LATTICES . . .
1 65 7.1 INTRODUCTION AND HISTORICAL REMARKS 165
7.1.1 LOCALIZATION IN CONFIGURATION SPACE 166
7.2 DISCRETE BREATHERS AND HOMOCLINIC DYNAMICS 168
7.2.1 HOW TO CONSTRUCT HOMOCLINIC ORBITS 171
7.3 A METHOD FOR CONSTRUCTING DISCRETE BREATHERS 174
7.3.1 STABILIZING DISCRETE BREATHERS BY A CONTROL METHOD 175
7.4 DISORDERED LATTICES 180
7.4.1 ANDERSON LOCALIZATION IN DISORDERED LINEAR M E D I A 180
7.4.2 DIFFUSION IN DISORDERED NONLINEAR CHAINS 183
7.4.2.1 TWO BASIC MODELS 183
7.4.2.2 REGIMES O F WAVE PACKET SPREADING 185
7.4.2.3 NUMERICAL RESULTS 186
EXERCISES 188
PROBLEMS 189
8 THE STATISTICAL MECHANICS O F QUASI-STATIONARY STATES 191
8.1 FROM DETERMINISTIC DYNAMICS TO STATISTICAL MECHANICS 191
8.1.1 NONEXTENSIVE STATISTICAL MECHANICS AND Y-GAUSSIAN PDFS 193
8.2 STATISTICAL DISTRIBUTIONS O F CHAOTIC Q S S AND THEIR COMPUTATION
195 8.3 FPU JR-MODE U N D E R PERIODIC BOUNDARY CONDITIONS 197
8.3.1 CHAOTIC BREATHERS AND THE F P U 7T-MODE 2 0 0
8.4 F P U S P O L AND S P 0 2 M O D E S U N D E R FIXED BOUNDARY
CONDITIONS 2 0 3
8.5 ^-GAUSSIAN DISTRIBUTIONS FOR A SMALL MICROPLASMA SYSTEM 2 0 8
8.6 CHAOTIC QUASI-STATIONARY STATES IN AREA-PRESERVING M A P S 2 1 2
8.6.1 TIME-EVOLVING STATISTICS O F PDFS IN AREA- PRESERVING MAPS 2 1 3
8.6.2 T H E PERTURBED MACMILLAN M A P 2 1 4
8.6.2.1 T H E S = 0.9, N = 1.6 CLASS O F EXAMPLES 2 1 5
8.6.2.2 T H E E - 1.2, /X = 1.6 CLASS O F EXAMPLES 2 1 7
EXERCISES 2 1 8
PROBLEMS 2 1 9
9 CONCLUSIONS, O P E N PROBLEMS A N D FUTURE OUTLOOK 22 1
9.1 CONCLUSIONS 221
9.2 OPEN PROBLEMS 2 2 4
9.2.1 SINGULARITY ANALYSIS: W H E R E MATHEMATICS MEETS PHYSICS 2 2 4
IMAGE 4
XX CONTENTS
9.2.2 NONLINEAR NORMAL MODES, QUASIPERIODICITY
AND LOCALIZATION 2 2 6
9.2.3 DIFFUSION, QUASI-STATIONARY STATES AND COMPLEX STATISTICS . . . 2
2 9 9.3 FUTURE OUTLOOK 231
9.3.1 ANOMALOUS HEAT CONDUCTION AND CONTROL O F H E A T FLOW 231
9.3.2 COMPLEX SOLITON DYNAMICS IN NONLINEAR PHOTONIC STRUCTURES 2 3 2
9.3.3 KINETIC THEORY O F HAMILTONIAN SYSTEMS AND APPLICATIONS TO PLASMA
PHYSICS 2 3 5
REFERENCES 2 3 9
INDEX 2 5 3
|
| any_adam_object | 1 |
| author | Mpuntēs, Tasos Skokos, Haris |
| author_facet | Mpuntēs, Tasos Skokos, Haris |
| author_role | aut aut |
| author_sort | Mpuntēs, Tasos |
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| dewey-ones | 530 - Physics |
| dewey-raw | 530.15539 |
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| dewey-sort | 3530.15539 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV040263745 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:20:17Z |
| institution | BVB |
| isbn | 9783642273049 9783642273056 3642273041 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025119462 |
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| owner_facet | DE-11 DE-19 DE-BY-UBM DE-703 |
| physical | XXIII, 255 S. graph. Darst. 24 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in synergetics Springer complexity |
| spelling | Mpuntēs, Tasos Verfasser aut Complex Hamiltonian dynamics Tassos Bountis ; Haris Skokos Berlin [u.a.] Springer 2012 XXIII, 255 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer series in synergetics Springer complexity Literaturangaben Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Nichtlineare Dynamik (DE-588)4126141-0 s DE-604 Skokos, Haris Verfasser aut Erscheint auch als Online-Ausgabe Complex Hamiltonian Dynamics DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025119462&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mpuntēs, Tasos Skokos, Haris Complex Hamiltonian dynamics Nichtlineare Dynamik (DE-588)4126141-0 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4126141-0 (DE-588)4139943-2 |
| title | Complex Hamiltonian dynamics |
| title_auth | Complex Hamiltonian dynamics |
| title_exact_search | Complex Hamiltonian dynamics |
| title_full | Complex Hamiltonian dynamics Tassos Bountis ; Haris Skokos |
| title_fullStr | Complex Hamiltonian dynamics Tassos Bountis ; Haris Skokos |
| title_full_unstemmed | Complex Hamiltonian dynamics Tassos Bountis ; Haris Skokos |
| title_short | Complex Hamiltonian dynamics |
| title_sort | complex hamiltonian dynamics |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Nichtlineare Dynamik Hamiltonsches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025119462&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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