Nonlinear dynamics: non-integrable systems and chaotic dynamics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2017]
|
| Schriftenreihe: | De Gruyter studies in mathematical physics
volume 36 |
| Schlagworte: | |
| Online-Zugang: | Verlag Inhaltsverzeichnis |
| Beschreibung: | XIV, 283 Seiten Illustrationen, Diagramme, Porträts |
| ISBN: | 9783110439380 9783110430592 |
Internformat
MARC
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| 100 | 1 | |a Borisov, Alexander B. |d 1947- |e Verfasser |0 (DE-588)1120729378 |4 aut | |
| 245 | 1 | 0 | |a Nonlinear dynamics |b non-integrable systems and chaotic dynamics |c Alexander B. Borisov, Vladimir V. Zverev |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2017] | |
| 264 | 4 | |c © 2017 | |
| 300 | |a XIV, 283 Seiten |b Illustrationen, Diagramme, Porträts | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematical physics |v volume 36 | |
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Datensatz im Suchindex
| _version_ | 1804176114952699904 |
|---|---|
| adam_text | CONTENTS
1 NONLINEAR OSCILLATIONS * 1
1.1 NONLINEAR OSCILLATIONS OF A CONSERVATIVE SINGLE-DEGREE-OF-FREEDOM
SYSTEM* 3
1.1.1 QUALITATIVE DESCRIPTION OF MOTION BY THE PHASE PLANE
METHOD * 5
1.2 OSCILLATIONS OF A MATHEMATICAL PENDULUM. ELLIPTIC FUNCTIONS* 9
1.3 SMALL-AMPLITUDE OSCILLATIONS OF A CONSERVATIVE
SINGLE-DEGREE-OF-FREEDOM SYSTEM * 14
1.3.1 STRAIGHTFORWARD EXPANSION * 15
1.3.2 THE METHOD OF MULTIPLE SCALES * 18
1.3.3 THE METHOD OF AVERAGING: THE VAN DER POL EQUATION * 22
1.3.4 THE GENERALIZED METHOD OF AVERAGING. THE KRYLOV-
BOGOLYUBOV APPROACH * 24
1.4 FORCED OSCILLATIONS OF AN ANHARMONIC OSCILLATOR * 27
1.4.1 STRAIGHTFORWARD EXPANSION * 28
1.4.2 A SECONDARY RESONANCE AT
O)
3 * 29
1.4.3 A PRIMARY RESONANCE: AMPLITUDE-FREQUENCY
RESPONSE * 31
1.5 SELF-OSCILLATIONS: LIMIT CYCLES * 37
1.5.1 AN ANALYTICAL SOLUTION OF THE VAN DER POL EQUATION FOR SMALL
NONLINEARITY PARAMETER VALUES * 39
1.5.2 AN APPROXIMATE SOLUTION OF THE VAN DER POL EQUATION FOR
LARGE NONLINEARITY PARAMETER VALUES * 42
1.6 EXTERNAL SYNCHRONIZATION OF SELF-OSCILLATING SYSTEMS * 45
1.7 PARAMETRIC RESONANCE * 55
1.7.1 THE FLOQUET THEORY* 56
1.7.2 AN ANALYTICAL SOLUTION OF THE MATHIEU EQUATION FOR SMALL
NONLINEARITY PARAMETER VALUES * 60
2 I NTEGRABLE SYSTEMS * 65
2.1 EQUATIONS OF MOTION FOR A RIGID BODY* 65
2.1.1 EULER S ANGLES * 68
2.1.2 EULER*S KINEMATIC EQUATIONS * 71
2.1.3 MOMENT OF INERTIA OF A RIGID BODY* 73
2.1.4 EULER*S DYNAMIC EQUATIONS * 76
2.1.5 S.V. KOVALEVSKAYA*S ALGORITHM FOR INTEGRATING EQUATIONS OF
MOTION FOR A RIGID BODY ABOUT A FIXED POINT * 79
2.2 THE PAINLEVSS PROPERTY FOR DIFFERENTIAL EQUATIONS * 85
2.2.1 A BRIEF OVERVIEW OF THE ANALYTIC THEORY OF DIFFERENTIAL
EQUATIONS * 85
2.2.2 A MODERN ALGORITHM OF ANALYSIS OF INTEGRABLE
SYSTEMS * 88
2.2.3 INTEGRABILITY OF THE GENERALIZED HENON-HEILES MODEL * 94
2.2.4 THE LINEARIZATION METHOD FOR CONSTRUCTING PARTICULAR
SOLUTIONS OF A NONLINEAR MODEL* 98
2.3 DYNAMICS OF PARTICLES IN THE TODA LATTICE: INTEGRATION BY THE METHOD
OF
THE INVERSE SCATTERING PROBLEM * 100
2.3.1 LAX*S REPRESENTATION* 104
2.3.2 THE DIRECT SCATTERING PROBLEM * 108
2.3.3 THE INVERSE SCATTERING TRANSFORM* 116
2.3.4 N-SOLITON SOLUTIONS
-----
120
2.3.5 THE INVERSE SCATTERING PROBLEM AND THE RIEMANN
PROBLEM * 128
2.3.6 SOLITONS AS ELEMENTARY EXCITATIONS OF NONLINEAR INTEGRABLE
SYSTEMS * 133
2.3.7 THE DARBOUX-BACKLUND TRANSFORMATIONS* 135
2.3.8 MULTIPLICATION OF INTEGRABLE EQUATIONS: THE MODIFIED TODA
LATTICE * 139
3 STABILITY OF MOTION AND STRUCTURAL STABILITY * 145
3.1 STABILITY OF MOTION* 145
3.1.1 STABILITY OF FIXED POINTS AND TRAJECTORIES * 145
3.1.2 SUCCESSION MAPPING OR THE POINCARE MAP * 149
3.1.3 THEOREM ABOUT THE VOLUME OF A PHASE DROP * 151
3.1.4 POINCARE-BENDIXSON THEOREM AND TOPOLOGY OF THE PHASE
PLANE* 153
3.1.5 THE LYAPUNOV EXPONENTS * 155
3.2 STRUCTURAL STABILITY* 162
3.2.1 TOPOLOGICAL RECONSTRUCTION OF THE PHASE PORTRAIT* 162
3.2.2 COARSE SYSTEMS* 165
3.2.3 CUSP CATASTROPHE * 167
3.2.4 CATASTROPHE THEORY * 169
4 CHAOS IN CONSERVATIVE SYSTEMS * 174
4.1 DETERMINISM AND IRREVERSIBILITY * 174
4.2 SIMPLE MODELS WITH UNSTABLE DYNAMICS* 180
4.2.1 HOMOCLINIC STRUCTURE * 180
4.2.2 THE ANOSOV MAP * 182
4.2.3 THE TENT MAP * 183
4.2.4 THE BERNOULLI SHIFT * 187
4.3 DYNAMICS OF HAMILTONIAN SYSTEMS CLOSE TO INTEGRABLE* 189
4.3.1 PERTURBED MOTION AND NONLINEAR RESONANCE * 189
4.3.2 THE ZASLAVSKY-CHIRIKOV MAP * 193
4.3.3 CHAOS AND KOLMOGOROV-ARNOLD-MOSER THEORY * 195
5 CHAOS AND FRACTAL ATTRACTORS
IN DISSIPATIVE SYSTEMS * 200
5.1 ON THE NATURE OF TURBULENCE * 200
5.2 DYNAMICS OF THE LORENZ MODEL * 203
5.2.1 DISSIPATIVITY OF THE LORENZ MODEL * 205
5.2.2 BOUNDEDNESS OF THE REGION OF STATIONARY MOTION * 205
5.2.3 STATIONARY POINTS * 206
5.2.4 THE LORENZ MODEL*S DYNAMIC REGIMES AS A RESULT OF
BIFURCATIONS * 207
5.2.5 MOTION ON A STRANGE ATTRACTOR* 208
5.2.6 HYPOTHESIS ABOUT THE STRUCTURE OF A STRANGE
ATTRACTOR* 209
5.2.7 THE LORENZ MODEL AND THE TENT MAP * 211
5.2.8 LYAPUNOV EXPONENTS * 212
5.3 ELEMENTS OF CANTOR SET THEORY * 213
5.3.1 POTENTIAL AND ACTUAL INFINITY * 213
5.3.2 CANTOR*S THEOREM AND CARDINAL NUMBERS * 217
5.3.3 CANTOR SETS * 222
5.4 CANTOR STRUCTURE OF ATTRACTORS IN TWO-DIMENSIONAL MAPPINGS * 225
5.4.1 THE HENON MAP * 225
5.4.2 THE IKEDA MAP * 227
5.4.3 AN ANALYTICAL THEORY OF THE CANTOR STRUCTURE OF
ATTRACTORS * 228
5.5 MATHEMATICAL MODELS OF FRACTAL STRUCTURES * 230
5.5.1 MASSIVE CANTOR SET * 231
5.5.2 A BINOMIAL MULTIPLICATIVE PROCESS * 232
5.5.3 THE SPECTRUM OF FRACTAL DIMENSIONS * 237
5.5.4 THE LYAPUNOV DIMENSION * 240
5.5.5 A RELATIONSHIP BETWEEN THE MASS EXPONENT AND THE
SPECTRAL FUNCTION * 241
5.5.6 THE MASS EXPONENT OF THE MULTIPLICATIVE BINOMIAL
PROCESS * 243
5.5.7 A MULTIPLICATIVE BINOMIAL PROCESS ON A FRACTAL
CARRIER* 244
5.5.8 A TEMPORAL DATA SEQUENCE AS A SOURCE OF INFORMATION
ABOUT AN ATTRACTOR* 245
5.6 UNIVERSALITY AND SCALING IN THE DYNAMICS OF ONE-DIMENSIONAL MAPS *
249
5.6.1 GENERAL REGULARITIES OF A PERIOD-DOUBLING PROCESS * 250
5.6.2 THE FEIGENBAUM-CVITANOVIC EQUATION * 258
5.6.3 A UNIVERSAL REGULARITY IN THE ARRANGEMENT OF CYCLES: A
UNIVERSAL POWER SPECTRUM * 262
SYNCHRONIZATION OF CHAOTIC OSCILLATIONS * 269
5.7
XIV CONTENTS
5.7.1 SYNCHRONIZATION IN A SYSTEM OF TWO COUPLED MAPS * 270
5.7.2 TYPES AND CRITERIA OF SYNCHRONIZATION * 272
CONCLUSION* 274
REFERENCES
-----
277
INDEX* 281
|
| any_adam_object | 1 |
| author | Borisov, Alexander B. 1947- Zverev, Vladimir V. |
| author_GND | (DE-588)1120729378 (DE-588)1121511767 |
| author_facet | Borisov, Alexander B. 1947- Zverev, Vladimir V. |
| author_role | aut aut |
| author_sort | Borisov, Alexander B. 1947- |
| author_variant | a b b ab abb v v z vv vvz |
| building | Verbundindex |
| bvnumber | BV043488291 |
| classification_rvk | SK 950 UG 3900 |
| ctrlnum | (OCoLC)965803053 (DE-599)DNB1082767263 |
| dewey-full | 530 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530 |
| dewey-search | 530 |
| dewey-sort | 3530 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV043488291 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:27:03Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110439380 9783110430592 |
| language | English |
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| owner_facet | DE-11 DE-384 DE-703 DE-19 DE-BY-UBM DE-29T |
| physical | XIV, 283 Seiten Illustrationen, Diagramme, Porträts |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematical physics |
| series2 | De Gruyter studies in mathematical physics |
| spelling | Borisov, Alexander B. 1947- Verfasser (DE-588)1120729378 aut Nonlinear dynamics non-integrable systems and chaotic dynamics Alexander B. Borisov, Vladimir V. Zverev Berlin ; Boston De Gruyter [2017] © 2017 XIV, 283 Seiten Illustrationen, Diagramme, Porträts txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics volume 36 Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Nichtintegrables System (DE-588)4462790-7 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s Nichtintegrables System (DE-588)4462790-7 s DE-604 Nichtlineares dynamisches System (DE-588)4126142-2 s Mathematische Physik (DE-588)4037952-8 s 1\p DE-604 Zverev, Vladimir V. Verfasser (DE-588)1121511767 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, pdf 978-3-11-043058-5 Erscheint auch als Online-Ausgabe, epub 978-3-11-043067-7 De Gruyter studies in mathematical physics volume 36 (DE-604)BV040141722 36 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110439380&searchTitles=true Verlag DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028904872&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Borisov, Alexander B. 1947- Zverev, Vladimir V. Nonlinear dynamics non-integrable systems and chaotic dynamics De Gruyter studies in mathematical physics Nichtlineare Dynamik (DE-588)4126141-0 gnd Nichtintegrables System (DE-588)4462790-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| subject_GND | (DE-588)4126141-0 (DE-588)4462790-7 (DE-588)4037952-8 (DE-588)4126142-2 |
| title | Nonlinear dynamics non-integrable systems and chaotic dynamics |
| title_auth | Nonlinear dynamics non-integrable systems and chaotic dynamics |
| title_exact_search | Nonlinear dynamics non-integrable systems and chaotic dynamics |
| title_full | Nonlinear dynamics non-integrable systems and chaotic dynamics Alexander B. Borisov, Vladimir V. Zverev |
| title_fullStr | Nonlinear dynamics non-integrable systems and chaotic dynamics Alexander B. Borisov, Vladimir V. Zverev |
| title_full_unstemmed | Nonlinear dynamics non-integrable systems and chaotic dynamics Alexander B. Borisov, Vladimir V. Zverev |
| title_short | Nonlinear dynamics |
| title_sort | nonlinear dynamics non integrable systems and chaotic dynamics |
| title_sub | non-integrable systems and chaotic dynamics |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd Nichtintegrables System (DE-588)4462790-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| topic_facet | Nichtlineare Dynamik Nichtintegrables System Mathematische Physik Nichtlineares dynamisches System |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110439380&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028904872&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040141722 |
| work_keys_str_mv | AT borisovalexanderb nonlineardynamicsnonintegrablesystemsandchaoticdynamics AT zverevvladimirv nonlineardynamicsnonintegrablesystemsandchaoticdynamics AT walterdegruytergmbhcokg nonlineardynamicsnonintegrablesystemsandchaoticdynamics |