Physics of chaos in Hamiltonian systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Imperial College Press
1998
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 269 S. Ill., graph. Darst. |
| ISBN: | 1860940528 |
Staff View
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| 245 | 1 | 0 | |a Physics of chaos in Hamiltonian systems |c George M. Zaslavsky |
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| 300 | |a XII, 269 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804127149094862848 |
|---|---|
| adam_text | PHYSICS OF CHAOS IN HAMILTONIAN SYSTEMS GEORGE M. ZASLAVSKY DEPARTMENT
OF PHYSICS, NEW YORK UNIVERSITY COURANT INSTITUTE OF MATHEMATICAL
SCIENCES IMPERIAL COLLEGE PRESS CONTENTS PREFACE V 1 DISCRETE AND
CONTINUOUS MODELS 1 1.1 COEXISTENCE OF THE DYNAMICAL ORDER AND CHAOS 1
1.2 THE STANDARD MAP (KICKED ROTATOR) 3 1.3 THE WEB-MAP (KICKED
OSCILLATOR) 8 1.4 PERTURBED PENDULUM 14 1.5 PERTURBED OSCILLATOR 17 1.6
BILLIARDS 19 CONCLUSIONS 21 2 SEPARATRIX CHAOS 23 2.1 NONLINEAR
RESONANCE AND CHAIN OF ISLANDS 23 2.2 OVERLAPPING OF RESONANCES ^ 28 2.3
THE SEPARATRIX MAP 30 2.4 STOCHASTIC LAYER J 35 2.5 HIDDEN
RENORMALISATIORI GROUP NEAR THE SEPARATRIX 41 2.6 RENORMALISATION OF
RESONANCES 50 2.7 STOCHASTIC LAYER OF THE STANDARD MAP 51 CONCLUSIONS 54
3 THE PHASE SPACE OF CHAOS 56 3.1 NON-UNIVERSALITY OF THE SCENARIO 56
3.2 COLLAPSING ISLANDS ..- 63 3.3 BLINKING ISLANDS 69 3.4 BOUNDARY
ISLANDS 74 X CONTENTS 3.5 SELF-SIMILAR SET OF ISLANDS 76 3.6 GENERAL
COMMENTS ABOUT THE ISLAND 86 CONCLUSIONS * 86 4 NONLINEARITY VERSUS
PERTURBATION 88 4.1 BEYOND THE KAM-THEORY 88 4.2 WEB-TORI 90 4.3 WIDTH
OF THE STOCHASTIC WEB 98 4.4 TRANSITION FROM THE KAM-TORI TO WEB-TORI
100 CONCLUSIONS 103 5 FRACTALS AND CHAOS 105 5.1 FRACTAL DYNAMICS 105
5.2 GENERALISED FRACTAL DIMENSION 108 5.3 RENORMALISATION GROUP AND
GENERALISED FRACTAL DIMENSION 110 5.4 MULTI-FRACTAL SPECTRA 111
CONCLUSIONS 116 6 POINCARE RECURRENCES AND FRACTAL TIME 117 6.1 POINCARE
RECURRENCES 117 6.2 POISSONIAN DISTRIBUTION OF RECURRENCES 119 6.3
NON-ERGODICITY, STICKINESS AND QUASI-TRAPS * 122 6.4 RENORMALISATION
FORMULAS FOR THE EXIT TIME DISTRIBUTION , 128 6.5 FRACTAL TIME 132 6.6
FRACTAL AND MULTI-FRACTAL RECURRENCES 134 6.7 MULTI-FRACTAL SPACE-TIME
AND ITS DIMENSION SPECTRUM 138 6.8 CRITICAL EXPONENT FOR THE POINCARE
RECURRENCES 141 CONCLUSIONS 142 7 CHAOS AND FOUNDATION OF STATISTICAL
PHYSICS 144 7.1 THE DYNAMICAL FOUNDATION OF STATISTICAL PHYSICS 144 7.2
FRACTAL TRAPS AND MAXWELL S DEMON 146 CONTENTS XI 7.3 COUPLED BILLIARDS
152 7.4 CONTACTED CASSINI-SINAI BILLIARDS 159 CONCLUSIONS 166 COLOUR
PLATES (C.1-C.8) 8 CHAOS AND SYMMETRY 167 8.1 STOCHASTIC WEBS 167 8.2
STOCHASTIC WEB WITH QUASI-CRYSTALLINE SYMMETRY 170 8.3 STOCHASTIC WEB
SKELETON 174 8.4 SYMMETRIES AND THEIR DYNAMICAL TRANSFORMS 184 8.5 THE
WIDTH OF THE STOCHASTIC WEB 188 CONCLUSIONS 193 9 MORE DEGREES OF
FREEDOM 194 9.1 GENERAL REMARKS 194 9.2 FOUR-DIMENSIONAL MAP FOR THE
MOTION IN MAGNETIC FIELD 195 9.3 MULTI-WEB STRUCTURES IN THE PHASE SPACE
199 9.4 EQUILIBRIUM OF THE ATOMIC CHAINS 204 9.5 DISCRETISATION D 208
CONCLUSIONS S 211 10 NORMAL AND ANOMALOUS KINETICS 213 10.1
FOKKER-PLANCK-KOLMOGOROV (FPK) EQUATION 213 10.2 TRANSPORT FOR THE
STANDARD MAP AND WEB-MAP 218 10.3 DYNAMICS IN THE POTENTIAL WITH G-FOLD
SYMMETRY 222 10.4 MORE EXAMPLES OF THE ANOMALOUS TRANSPORT 225 10.5 LEVY
PROCESSES 228 10.6 THE WEIERSTRASS RANDOM WALK 231 CONCLUSIONS 233 11
FRACTIONAL KINETICS 234 11.1 FRACTIONAL GENERALISATION OF THE
FOKKER-PLANCK-KOLMOGOROV EQUATION (FFPK) 234 11.2 EVOLUTION OF MOMENTS
239 XII CONTENTS 11.3 METHOD OF THE RENORMALISATION GROUP FOR KINETICS
(RGK) 240 CONCLUSIONS ... 246 APPENDIX 1 THE NONLINEAR PENDULUM 247
APPENDIX 2 SOLUTION TO THE RENORMALISATION TRANSFORM EQUATION 251
APPENDIX 3 FRACTIONAL INTEGRO-DIFFERENTIATION 253 REFERENCES 257 INDEX
267
|
| any_adam_object | 1 |
| author | Zaslavsky, George M. 1935-2008 |
| author_GND | (DE-588)13657985X |
| author_facet | Zaslavsky, George M. 1935-2008 |
| author_role | aut |
| author_sort | Zaslavsky, George M. 1935-2008 |
| author_variant | g m z gm gmz |
| building | Verbundindex |
| bvnumber | BV012505956 |
| callnumber-first | Q - Science |
| callnumber-label | QC20 |
| callnumber-raw | QC20.7.H35 |
| callnumber-search | QC20.7.H35 |
| callnumber-sort | QC 220.7 H35 |
| callnumber-subject | QC - Physics |
| classification_rvk | UG 3900 |
| ctrlnum | (OCoLC)245677408 (DE-599)BVBBV012505956 |
| dewey-full | 514.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.74 |
| dewey-search | 514.74 |
| dewey-sort | 3514.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:28:45Z |
| institution | BVB |
| isbn | 1860940528 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008488193 |
| oclc_num | 245677408 |
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| owner | DE-355 DE-BY-UBR DE-703 |
| owner_facet | DE-355 DE-BY-UBR DE-703 |
| physical | XII, 269 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Zaslavsky, George M. 1935-2008 Verfasser (DE-588)13657985X aut Physics of chaos in Hamiltonian systems George M. Zaslavsky London Imperial College Press 1998 XII, 269 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hamiltonsches System - Chaotisches System Mathematische Physik Chaotic behavior in systems Hamiltonian systems Mathematical physics Chaos (DE-588)4191419-3 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Chaostheorie (DE-588)4009754-7 s DE-604 Chaos (DE-588)4191419-3 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008488193&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zaslavsky, George M. 1935-2008 Physics of chaos in Hamiltonian systems Hamiltonsches System - Chaotisches System Mathematische Physik Chaotic behavior in systems Hamiltonian systems Mathematical physics Chaos (DE-588)4191419-3 gnd Hamiltonsches System (DE-588)4139943-2 gnd Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4191419-3 (DE-588)4139943-2 (DE-588)4009754-7 |
| title | Physics of chaos in Hamiltonian systems |
| title_auth | Physics of chaos in Hamiltonian systems |
| title_exact_search | Physics of chaos in Hamiltonian systems |
| title_full | Physics of chaos in Hamiltonian systems George M. Zaslavsky |
| title_fullStr | Physics of chaos in Hamiltonian systems George M. Zaslavsky |
| title_full_unstemmed | Physics of chaos in Hamiltonian systems George M. Zaslavsky |
| title_short | Physics of chaos in Hamiltonian systems |
| title_sort | physics of chaos in hamiltonian systems |
| topic | Hamiltonsches System - Chaotisches System Mathematische Physik Chaotic behavior in systems Hamiltonian systems Mathematical physics Chaos (DE-588)4191419-3 gnd Hamiltonsches System (DE-588)4139943-2 gnd Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | Hamiltonsches System - Chaotisches System Mathematische Physik Chaotic behavior in systems Hamiltonian systems Mathematical physics Chaos Hamiltonsches System Chaostheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008488193&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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