Order and chaos in dynamical astronomy:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Physics and astronomy online library
Astronomy and astrophysics library |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 624 S. graph. Darst. |
| ISBN: | 3540433600 |
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Datensatz im Suchindex
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|---|---|
| adam_text | GEORGE CONTOPOULOS ORDER AND CHAOS IN DYNAMICAL ASTRONOMY WITH 305
FIGURES SPRINGER CONTENTS 1. HISTORICAL INTRODUCTION 1 1.1 CELESTIAL
MECHANICS 1 1.2 STATISTICAL MECHANICS 2 1.3 DYNAMICAL ASTRONOMY 3 1.4
COMPUTER EXPERIMENTS 4 1.5 THE THIRD INTEGRAL 5 1.6 ORDER AND CHAOS 6
1.7 APPLICATIONS TO GALAXIES 8 1.8 OTHER APPLICATIONS 9 2. ORDER AND
CHAOS IN GENERAL 11 2.1 TERMINOLOGY AND CLASSIFICATION 11 2.1.1
DYNAMICAL SYSTEMS 11 2.1.2 INTEGRABLE, CHAOTIC, ERGODIC, MIXING,
KOLMOGOROV AND ANOSOV SYSTEMS 13 2.1.3 OLD AND NEW CLASSIFICATION 17 2.2
INTEGRABLE SYSTEMS 20 2.2.1 EXAMPLES OF INTEGRABLE SYSTEMS 20, 2.2.2
SEPARABLE SYSTEMS. 25 2.2.3 TIME DEPENDENT SYSTEMS 27 2.2.4 INTEGRALS IN
VELOCITY-DEPENDENT POTENTIALS AND IN MAPS 29 2.2.5 STACKEL POTENTIALS IN
2 DIMENSIONS 30 2.2.6 A ROTATING STACKEL MODEL 36 2.2.7 STACKEL
POTENTIALS IN 3 DIMENSIONS 37 2.2.8 THE TODA LATTICE 42 2.2.9 PAINLEVE
ANALYSIS 46 2.2.10 CHECK OF INTEGRABILITY 48 2.3 THE THIRD INTEGRAL 49
2.3.1 FORMAL INTEGRALS 49 2.3.2 RESONANCE CASES 54 2.3.3 CONSTRUCTION OF
THE INTEGRALS AND OF THE NORMAL FORMS 58 2.3.4 THE PROBLEM OF
CONVERGENCE . 62 X CONTENTS 2.3.5 KAM THEORY 67 2.3.6 NEKHOROSHEV
THEORY 71 2.3.7 SUPEREXPONENTIAL STABILITY 74 2.3.8 DESTRUCTION OF THE
INTEGRALS 75 2.3.9 THE THIRD INTEGRAL IN PERIODIC POTENTIALS 78 2.3.10
ADIABATIC INVARIANTS 82 2.3.11 OTHER TYPES OF INTEGRALS 86 2.3.12
RATIONAL SOLUTIONS. THE PRENDERGAST METHOD 88 2.3.13 THE AVERAGING
METHOD 92 2.4 PERIODIC ORBITS 93 2.4.1 SURFACES OF SECTION 93 2.4.2
STABLE AND UNSTABLE PERIODIC ORBITS 97 2.4.3 BIFURCATIONS 101 2.4.4
CHARACTERISTICS 106 2.4.5 THE POINCARE-BIRKHOFF THEOREM ILL 2.4.6
THEORETICAL COMPUTATION OF PERIODIC ORBITS 115 2.5 SYSTEMS OF TWO
DEGREES OF FREEDOM 122 2.5.1 FORMS OF THE ORBITS 122 2.5.2 INVARIANT
CURVES 126 2.5.3 CHAOTIC ORBITS 129 2.5.4 RESONANT ISLANDS . 133 2.5.5
ROTATION NUMBERS 139 2.5.6 ASYMPTOTIC CURVES AND HOMOCLINIC POINTS 144
2.5.7 SMALE HORSESHOES 151 2.5.8 POINCARE RECURRENCE 154 2.5.9
DISTRIBUTION OF PERIODIC ORBITS 158 2.6 TRANSITION FROM ORDER TO CHAOS
168 2.6.1 THE LOGISTIC MAP 168 2.6.2 DISSIPATIVE AND CONSERVATIVE
SYSTEMS 173 2.6.3 ROUTES TO CHAOS 18Q 2.6.4 RESONANCE OVERLAP 185 2.7
THE LAST KAM TORUS 192 2.7.1 PROPERTIES OF THE LAST KAM TORUS 192 2.7.2
METHODS FOR LOCATING THE LAST KAM TORUS 196 2.7.3 CANTORI AND STICKINESS
203 2.7.4 DESTRUCTION OF THE ISLANDS OF STABILITY 213 2.8 LARGE
PERTURBATIONS 220 2.8.1 HETEROCLINIC POINTS 220 2.8.2 SYSTEMS WITHOUT
ESCAPES ! 222 2.8.3 THE ANISOTROPIC KEPLER PROBLEM 227 2.8.4 CONVERSE
KAM THEORY AND THE ANTI-INTEGRABILITY LIMIT 227 2.8.5 NORMAL DIFFUSION
AND ANOMALOUS DIFFUSION 228 2.8.6 LINEAR ERGODIC SYSTEMS 233 CONTENTS XI
2.9 SYSTEMS WITH ESCAPES 237 2.9.1 TRANSITION TO ESCAPE 237 2.9.2 BASINS
OF ESCAPE AND ESCAPE TIMES 244 2.9.3 CHAOTIC SCATTERING 248 2.10
DYNAMICAL SPECTRA 251 2.10.1 LYAPUNOV CHARACTERISTIC NUMBERS 251 2.10.2
SPECTRA OF STRETCHING NUMBERS 257 2.10.3 ANGULAR SPECTRA 262 2.10.4
EXPLANATION OF THE FORMS OF THE SPECTRA 265 2.10.5 DISTINCTION BETWEEN
ORDERED AND CHAOTIC MOTIONS .. 270 2.10.6 FREQUENCY ANALYSIS 274 2.10.7
COMPARISON OF VARIOUS METHODS 277 2.10.8 SPECTRA OF LINEAR SYSTEMS 280
2.10.9 CHAOS VS. RANDOMNESS AND NOISE 280 2.10.10 ACCURACY OF NUMERICAL
ORBITS. SHADOWING 283 2.11 SYSTEMS OF THREE DEGREES OF FREEDOM 284
2.11.1 PERIODIC ORBITS AND STABILITY TYPES 284 2.11.2 BIFURCATIONS AND
THEIR COLLISIONS 290 2.11.3 THE KREIN-MOSER THEOREM 298 2.11.4 SIMPLE
RESONANT 3-D SYSTEMS 300 2.11.5 QUALITATIVE CHANGES IN 3-D SYSTEMS 304
2.11.6 COMPLEX INSTABILITY ; 308 2.11.7 TERMINATION OF SEQUENCES OF
BIFURCATIONS 315 2.11.8 DISTRIBUTION OF PERIODIC ORBITS 318 2.11.9
PERIODIC AND NONPERIODIC ORBITS DERIVED THEORETICALLY 322 2.11.10
ORDERED AND CHAOTIC DOMAINS 327 2.11.11 4-D SURFACES OF SECTION 332
2.11.12 NONPERIODIC ORBITS IN 4-D MAPS 335 2.11.13 SPECTRA OF 4-D MAPS
339 2.11.14 ARNOLD DIFFUSION . . . 344 2.12 SYSTEMS OF N DEGREES OF
FREEDOM 351 2.12.1 THE FERMI-PASTA-ULAM PROBLEM 351 2.12.2 N-BODY CHAINS
354 2.12.3 RESONANT AND NONRESONANT MODES 358 2.12.4 A CLASSICAL PLANCK
SPECTRUM 360 2.12.5 LYAPUNOV CHARACTERISTIC NUMBERS AND SPECTRA OF
N-BODY SYSTEMS 362 2.12.6 SOLITONS IN DISCRETE SYSTEMS 364 2.12.7
GEODESIC FLOWS 366 2.13 FRACTALS 369 2.13.1 SIMPLE FRACTALS 369 2.13.2
GENERALIZED DIMENSIONS 373 2.13.3 MULTIFRACTALS 375 XII CONTENTS 3.
ORDER AND CHAOS IN GALAXIES 377 3.1 ORBITS IN 2-D GALAXIES 377 3.1.1
TYPES OF ORBITS. THE MAIN RESONANCES 377 3.1.2 EPICYCLIC ORBITS 381
3.1.3 AXISYMMETRIC AND NONAXISYMMETRIC MODELS 385 3.1.4 THE MAIN
FAMILIES OF PERIODIC ORBITS 390 3.1.5 SHORT AND LONG PERIOD ORBITS 404
3.1.6 NONPERIODIC ORBITS 410 3.1.7 RINGS, SHOCKS AND VORTICES 416 3.1.8
LOCATING COROTATION 419 3.1.9 ESCAPING ORBITS 420 3.2 ORBITS IN 3-D
GALAXIES 422 3.2.1 THE MAIN FAMILIES OF ORBITS 422 3.2.2 POLAR RINGS 426
3.2.3 WARPED AND BUCKLED GALAXIES 428 3.2.4 PEANUT AND BOX GALAXIES 430
3.2.5 CHAOTIC ORBITS IN GALAXIES 432 3.3 THEORETICAL ORBITS IN GALAXIES
433 3.3.1 INTEGRABLE AND NONINTEGRABLE GALACTIC MODELS 433 3.3.2 THIRD
INTEGRAL IN THE MERIDIAN PLANE 434 3.3.3 THIRD INTEGRAL IN SPIRAL AAD
BARRED GALAXIES 436 3.3.4 INTEGRALS NEAR COROTATION 447 3.3.5
THEORETICAL EXPLANATION OF THE BIFURCATIONS AND GAPS 455 3.3.6 THE
NONLINEAR DENSITY WAVE THEORY 461 3.3.7 THE RESPONSE DENSITY 467 3.3.8
TERMINATION OF BARS AND SPIRALS 473 3.3.9 PREFERENCE OF TRAILING WAVES
477 3.3.10 THIRD INTEGRALS IN N-BODY SYSTEMS 479 3.3.11 ORBITS IN
PERIODIC POTENTIALS 486 3.3.12 ORBITS IN EVOLVING GALAXIES 489- 3.4
SELF-CONSISTENT MODELS 490 3.4.1 ANALYTICAL METHODS 490 3.4.2 THE
SCHWARZSCHILD METHOD AND ITS VARIANTS 492 3.4.3 SELF-CONSISTENT MODELS
OF ELLIPTICAL GALAXIES 494 3.4.4 SELF-CONSISTENT MODELS OF SPIRAL
GALAXIES 497 3.4.5 SELF-CONSISTENT MODELS OF BARRED GALAXIES 502 3.5
IV-BODY SYSTEMS 503 3.5.1 METHODS OF IV-BODY SIMULATIONS 503 3.5.2
COLLISIONAL AND COLLISIONLESS RELAXATION 506 3.5.3 VIOLENT RELAXATION
AND LYNDEN-BELL STATISTICS 513 3.5.4 DISTRIBUTION FUNCTIONS FOR
SPHERICAL JV-BODY SYSTEMS 516 3.5.5 MEMORY OF INITIAL CONDITIONS 518
CONTENTS XIII 3.5.6 COUNTERROTATING GALAXIES 520 3.5.7 A ONE-DIMENSIONAL
GRAVITATIONAL GAS 521 3.5.8 GRAVOTHERMAL CATASTROPHE 524 3.5.9 GLOBAL
DYNAMICS OF GALAXIES 527 3.6 DYNAMICAL SPECTRA OF GALAXIES 529 3.6.1
DYNAMICAL SPECTRA OF HAMILTONIAN SYSTEMS 529 3.6.2 DYNAMICAL SPECTRA OF
OSCILLATING GALAXIES 533 3.6.3 FREQUENCY ANALYSIS IN GALAXIES 535 4.
OTHER APPLICATIONS IN DYNAMICAL ASTRONOMY 539 4.1 ORDER AND CHAOS IN THE
SOLAR SYSTEM 539 4.1.1 ORDER AND CHAOS IN THE RESTRICTED THREE-BODY
PROBLEM 539 4.1.2 THE TROJAN ASTEROIDS 543 4.1.3 THE SITNIKOV PROBLEM
544 4.1.4 THE GENERAL THREE BODY PROBLEM. COLLISIONS 546 4.1.5 CHAOS IN
THE SOLAR SYSTEM 549 4.1.6 GAPS IN THE DISTRIBUTION OF ASTEROIDS 552
4.1.7 STABLE CHAOS 554 4.1.8 LYAPUNOV TIME AND MACROSCOPIC INSTABILITY
TIME . . . 555 4.2 RELATIVISTIC CHAOS 556 4.2.1 CHAOS IN THE CASE OF TWO
FIXED BLACK HOLES 556 4.2.2 COMPARISON WITH THE CLASSICAL THEORY 564
4.2.3 CHAOS IN VARIOUS RELATIVISTIC PROBLEMS 567 4.3 CHAOTIC COSMOLOGY
568 4.3.1 THE MIXMASTER COSMOLOGY 568 4.3.2 THE NONINTEGRABILITY OF THE
MIXMASTER MODEL 569 4.3.3 CHAOS AND ORDER IN OTHER COSMOLOGICAL MODELS
572 APPENDIX A 575 APPENDIX B 579 SOME OPEN PROBLEMS 583 REFERENCES 587
INDEX 619
|
| any_adam_object | 1 |
| author | Kontopulos, Geōrgios Iōannu 1928- |
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| discipline | Physik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:01:37Z |
| institution | BVB |
| isbn | 3540433600 |
| language | English |
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| spelling | Kontopulos, Geōrgios Iōannu 1928- Verfasser (DE-588)121398293 aut Order and chaos in dynamical astronomy George Contopoulos Berlin [u.a.] Springer 2002 XIII, 624 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics and astronomy online library Astronomy and astrophysics library Himmelsmechanik (DE-588)4127484-2 gnd rswk-swf Astronomie (DE-588)4003311-9 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Stellardynamik (DE-588)4130273-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Himmelsmechanik (DE-588)4127484-2 s Chaotisches System (DE-588)4316104-2 s DE-604 Stellardynamik (DE-588)4130273-4 s Astronomie (DE-588)4003311-9 s Dynamisches System (DE-588)4013396-5 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009823446&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kontopulos, Geōrgios Iōannu 1928- Order and chaos in dynamical astronomy Himmelsmechanik (DE-588)4127484-2 gnd Astronomie (DE-588)4003311-9 gnd Chaotisches System (DE-588)4316104-2 gnd Stellardynamik (DE-588)4130273-4 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4127484-2 (DE-588)4003311-9 (DE-588)4316104-2 (DE-588)4130273-4 (DE-588)4013396-5 |
| title | Order and chaos in dynamical astronomy |
| title_auth | Order and chaos in dynamical astronomy |
| title_exact_search | Order and chaos in dynamical astronomy |
| title_full | Order and chaos in dynamical astronomy George Contopoulos |
| title_fullStr | Order and chaos in dynamical astronomy George Contopoulos |
| title_full_unstemmed | Order and chaos in dynamical astronomy George Contopoulos |
| title_short | Order and chaos in dynamical astronomy |
| title_sort | order and chaos in dynamical astronomy |
| topic | Himmelsmechanik (DE-588)4127484-2 gnd Astronomie (DE-588)4003311-9 gnd Chaotisches System (DE-588)4316104-2 gnd Stellardynamik (DE-588)4130273-4 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Himmelsmechanik Astronomie Chaotisches System Stellardynamik Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009823446&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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