Nonlinearities in action: oscillations, chaos, order, fractals
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1992
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | XI, 191 S. Ill., graph. Darst. |
| ISBN: | 3540519882 0387519882 |
Internformat
MARC
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| 100 | 1 | |a Gaponov-Grechov, Andrej V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinearities in action |b oscillations, chaos, order, fractals |c A. V. Gaponov-Grekhov ; M. I. Rabinovich |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1992 | |
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Datensatz im Suchindex
| _version_ | 1804119655327989760 |
|---|---|
| adam_text | CONTENTS 1. INTRODUCTION 1 2. NONLINEAR OSCILLATIONS AND WAVES.
CLASSICAL RESULTS 11 2.1 OSCILLATORS 11 2.1.1 A MARBLE IN THE CHUTE 11
2.1.2 SPRING PENDULUM AND NONLINEAR OPTICS . 14 2.1.3 NONLINEAR LANDAU
DAMPING AND AMPLIFICATION 18 2.2 SOLITONS 22 2.2.1 THE FERMI-PASTA-ULAM
PARADOX 22 2.2.2 SOLITONS AS PARTICLES 25 2.2.3 SOLITONS AND SHOCK WAVES
27 2.3 SELF-EXCITED OSCILLATIONS 31 2.3.1 EXAMPLES AND DEFINITIONS 32
2.3.2 COMPETITION AND SYNCHRONIZATION 36 2.3.3 SELF-EXCITED OSCILLATIONS
IN CHAINS AND CONTINUOUS SYSTEMS 38 2.4 BIFURCATIONS 40 2.4.1
ACQUISITION OF A NEW QUALITY 40 2.4.2 BIFURCATIONS OF EQUILIBRIUM STATES
43 2.4.3 BIFURCATIONS OF PERIODIC MOTION 45 2.4.4 BIFURCATIONS - CHANGES
OF STABILITY IN PERIODIC MOTION . 45 2.5 MODULATION 46 2.5.1 THE ROLE OF
SMALL PARAMETERS 46 2.5.2 RUNNING MANDELSTAM LATTICES. MODULATION OF
WAVES BY WAVES 48 2.5.3 GENERATION OF MODULATION 51 2.5.4
SELF-MODULATION 52 2.5.5 RECURRENCE 54 2.5.6 MODULATION SOLITONS 56 3.
CHAOS 59 3.1 HISTORICAL REMARKS 59 3.2 MARBLE IN AN OSCILLATING CHUTE 60
3.3 STOCHASTIC SELF-EXCITED OSCILLATIONS 64 3.3.1 THE LORENZ ATTRACTOR
65 3.3.2 SYNCHRONIZATION - BEATS - CHAOS 68 3.3.3 AUTONOMOUS NOISE
GENERATOR 69 3.3.4 SCENARIOS FOR THE BIRTH OF STRANGE ATTRACTORS 72 3.4
CHAOS AND NOISE 75 3.4.1 DIMENSION AND ENTROPY 75 3.4.2 THE CANTOR
STRUCTURE OF A STRANGE ATTRACTOR 76 3.4.3 DIMENSION AND LYAPUNOV
EXPONENT .... 78 3.4.4 DETERMINISTICALLY GENERATED AND RANDOM SIGNALS 81
STRUCTURES 85 4.1 ORDER AND DISORDER - EXAMPLES 85 4.2 ATTRACTORS AND
SPATIAL PATTERNS 90 4.2.1 EXAMPLES OF EQUATIONS 90 4.2.2 MULTISTABILITY.
DEFECTS 92 4.3 SELF-STRUCTURES 98 4.3.1 CONVECTIVE SELF-STRUCTURES 98
4.3.2 LOCALIZATION MECHANISMS 100 4.3.3 SELF-STRUCTURES IN
THREE-DIMENSIONAL MEDIA 101 4.3.4 INTERACTION OF ELEMENTARY PARTICLES
. . . 103 4.3.5 BIRTH AND INTERACTION OF SPIRAL WAVES . . . 105 4.4
ATTRACTORS - MEMORY - LEARNING 107 4.4.1 HOW TO REMEMBER 107 4.4.2
CAMERA + TV + FEEDBACK ANALOGUE . . 109 4.4.3 CRITICAL PHENOMENA 112
4.4.4 STRUCTURES IN NEURON-LIKE MEDIA 113 TURBULENCE 117 5.1 PREHISTORY
117 5.2 BASIC MODELS OF DYNAMIC THEORY 120 5.3 TURBULENCE AND STRUCTURES
IN TWO-DIMENSIONAL FIELDS 122 5.3.1 EXPERIMENTS 122 5.3.2 DEVELOPMENT OF
TURBULENCE AND MULTI-DIMENSIONAL ATTRACTORS 125 5.4 SPATIAL EVOLUTION OF
TURBULENCE 127 5.4.1 FLOW DIMENSION 127 5.4.2 SPATIAL BIFURCATIONS 129
5.5 DISCUSSION 130 NONLINEAR PHYSICS - CHAOS AND ORDER 133 6.1 THE WHERE
AND THE HOW 133 6.2 RANDOMNESS BORN OUT OF NONRANDOMNESS 134 6.3 AN
UNSTABLE PATH AND STEADY MOTION. ARE THEY INCOMPATIBLE? 136 6.4 DOES
CHANCE RULE THE WORLD? 137 6.5 WHAT IS THE CHARACTER OF NATURE? INTEGER
OR FRACTAL? 139 6.6 FRACTAL FINGERS 141 6.7 SELF-ORGANIZING STRUCTURES
143 6.8 SINGLES 145 6.9 THE NEW LIFE OF AN OLD PROBLEM 145 6.10 SPATIAL
EVOLUTION OF DISORDER 146 6.11 WHAT DOES YOUR CAMERA SEE WHEN IT IS
WATCHING TV? 147 6.12 MULTISTABILITY AND MEMORY 148 6.13 NONLINEAR
DYNAMICS IN SOCIETY 149 COLOR PLATES 151 LITERATURE 177 ACKNOWLEDGEMENTS
OF THE FIGURES 185 SUBJECT INDEX 187
|
| any_adam_object | 1 |
| author | Gaponov-Grechov, Andrej V. Rabinovič, Michail I. |
| author_facet | Gaponov-Grechov, Andrej V. Rabinovič, Michail I. |
| author_role | aut aut |
| author_sort | Gaponov-Grechov, Andrej V. |
| author_variant | a v g g avg avgg m i r mi mir |
| building | Verbundindex |
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| dewey-ones | 530 - Physics |
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| dewey-sort | 3530.15 |
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| discipline | Physik Mathematik |
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| indexdate | 2024-07-09T16:29:38Z |
| institution | BVB |
| isbn | 3540519882 0387519882 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003406614 |
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| physical | XI, 191 S. Ill., graph. Darst. |
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| spelling | Gaponov-Grechov, Andrej V. Verfasser aut Nonlinearities in action oscillations, chaos, order, fractals A. V. Gaponov-Grekhov ; M. I. Rabinovich Berlin u.a. Springer 1992 XI, 191 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Russ. übers. Mathematical physics Nonlinear theories Mathematische Physik Nichtlineares Phänomen (DE-588)4136065-5 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Nichtlineare Theorie (DE-588)4251279-7 gnd rswk-swf Nichtlineares Phänomen (DE-588)4136065-5 s DE-604 Nichtlineare Theorie (DE-588)4251279-7 s Mathematische Physik (DE-588)4037952-8 s Nichtlineares dynamisches System (DE-588)4126142-2 s Rabinovič, Michail I. Verfasser aut OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003406614&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gaponov-Grechov, Andrej V. Rabinovič, Michail I. Nonlinearities in action oscillations, chaos, order, fractals Mathematical physics Nonlinear theories Mathematische Physik Nichtlineares Phänomen (DE-588)4136065-5 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Nichtlineare Theorie (DE-588)4251279-7 gnd |
| subject_GND | (DE-588)4136065-5 (DE-588)4126142-2 (DE-588)4037952-8 (DE-588)4251279-7 |
| title | Nonlinearities in action oscillations, chaos, order, fractals |
| title_auth | Nonlinearities in action oscillations, chaos, order, fractals |
| title_exact_search | Nonlinearities in action oscillations, chaos, order, fractals |
| title_full | Nonlinearities in action oscillations, chaos, order, fractals A. V. Gaponov-Grekhov ; M. I. Rabinovich |
| title_fullStr | Nonlinearities in action oscillations, chaos, order, fractals A. V. Gaponov-Grekhov ; M. I. Rabinovich |
| title_full_unstemmed | Nonlinearities in action oscillations, chaos, order, fractals A. V. Gaponov-Grekhov ; M. I. Rabinovich |
| title_short | Nonlinearities in action |
| title_sort | nonlinearities in action oscillations chaos order fractals |
| title_sub | oscillations, chaos, order, fractals |
| topic | Mathematical physics Nonlinear theories Mathematische Physik Nichtlineares Phänomen (DE-588)4136065-5 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Nichtlineare Theorie (DE-588)4251279-7 gnd |
| topic_facet | Mathematical physics Nonlinear theories Mathematische Physik Nichtlineares Phänomen Nichtlineares dynamisches System Nichtlineare Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003406614&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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