Dynamical chaos - basic concepts:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Leipzig
Teubner
1987
|
| Edition: | 1. Aufl. |
| Series: | Teubner-Texte zur Physik
14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zsfassung in franz., span. und russ. Sprache |
| Physical Description: | 172 S. graph. Darst. |
| ISBN: | 3322005054 |
Staff View
MARC
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| 245 | 1 | 0 | |a Dynamical chaos - basic concepts |c V. S. Anishchenko |
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Record in the Search Index
| _version_ | 1804116588214878208 |
|---|---|
| adam_text | Contents
Foreword by Editor 5
Author 8 Preface 7
1. General Review of the Problems Arising from Concept
of the Strange Attractor 10
1.1. Introduction 10
1.2. The Dynamical System and its Mathematical Model 10
1.3. Kinematical Interpretation of the Set of the
Differential Equations 12
1.4. Classification of the Dynamical Systems 14
1.5. Oscillatory Systems and their Properties 16
1.6. Phase Portraits of the Nonautooscillatory Systems 19
1.7. Autooscillatory Systems 28
1.8. Simple and Strange Attractors of the Dynamical
Systems 30
1.9. Signs of Stochastic Oscillations which can be
Visualized Experimentally 34
1.10. How the Chance Appears in the Deterministic
Systems 38
1.11. The Problem of Statistical Description of the
Dynamical Systems. Ergodic Theory 41
1.12. Analysis of the Dynamical Chaos in Presence of
Fluctuations 47
2. Elements of the Theory of Stability and
Bifurcations in the Dynamical Systems 52
2.1. Introduction 52
2.2. Stability in the Linear Approximation. Equations
in Variations 54
2.3. Lyapunov Characteristic Exponents for a Linear
System 56
2.4. Analysis of Stability of the Equilibrium States 60
2.5. Stability of Periodic Solutions. Floquet Theory 60
2.6. LCE Spectrum of the Strange Attractor 63
2.7. Poincare Map. Systems with Discrete Time
(Cascades) 65
2.8. Bifurcations of Stationary and Periodic Motions 69
2.9. Geometrical Structure and Dimension of the
Strange Attractors 83
2.10. Bifurcations of the Attractors 92
3. Mechanisms of Evolution and Criteria of the
Dynamical Chaos 96
3.1. Introduction 96
3.2. Route to Chaos through Period doubling
Bifurcation Cascade. Feigenbaum Regularity 98
3.3. Transition via Intermittency 107
3.4. Homoolinic Trajectories as a Criterium for the
Complexity of Dynamics. Shilnikov s Theorem 111
3.5. Routes to Chaos via Bifurcations of Quasiperiodic
Oscillations 116
4. Numerical Methods for the Study of the Nonlinear
System s Dynamics 128
4.1. Introduction 128
4.2. Computation of Poincare Maps 130
4.3. Numerical Analysis of Periodic Solutions and
of their Bifurcations 138
4.4. Numerical Analysis of the Statistical Properties
of the Attractors 147
4.5. Algorithms of ICE Spectrum Calculation 153
4.6. Numerical Construction of One dimensional
Separatrices and Separatrii Contours 158
5. References 165
|
| any_adam_object | 1 |
| author | Aniščenko, Vadim S. 1943- |
| author_GND | (DE-588)111580080 |
| author_facet | Aniščenko, Vadim S. 1943- |
| author_role | aut |
| author_sort | Aniščenko, Vadim S. 1943- |
| author_variant | v s a vs vsa |
| building | Verbundindex |
| bvnumber | BV002134230 |
| callnumber-first | Q - Science |
| callnumber-label | Q172 |
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| callnumber-search | Q172.5.C45 |
| callnumber-sort | Q 3172.5 C45 |
| callnumber-subject | Q - General Science |
| classification_rvk | SK 820 UG 3900 |
| classification_tum | MAT 587f PHY 066f |
| ctrlnum | (OCoLC)18469535 (DE-599)BVBBV002134230 |
| dewey-full | 003/.7 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003/.7 |
| dewey-search | 003/.7 |
| dewey-sort | 13 17 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Physik Informatik Mathematik |
| edition | 1. Aufl. |
| format | Book |
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| id | DE-604.BV002134230 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:53Z |
| institution | BVB |
| isbn | 3322005054 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001399554 |
| oclc_num | 18469535 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-703 DE-739 DE-355 DE-BY-UBR DE-384 DE-634 DE-83 DE-11 |
| owner_facet | DE-91 DE-BY-TUM DE-703 DE-739 DE-355 DE-BY-UBR DE-384 DE-634 DE-83 DE-11 |
| physical | 172 S. graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Physik |
| series2 | Teubner-Texte zur Physik |
| spelling | Aniščenko, Vadim S. 1943- Verfasser (DE-588)111580080 aut Dynamical chaos - basic concepts V. S. Anishchenko 1. Aufl. Leipzig Teubner 1987 172 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Physik 14 Zsfassung in franz., span. und russ. Sprache Chaotic behavior in systems Differentiable dynamical systems Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s DE-604 Chaostheorie (DE-588)4009754-7 s Chaos (DE-588)4191419-3 s Dynamisches System (DE-588)4013396-5 s Teubner-Texte zur Physik 14 (DE-604)BV000019271 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001399554&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aniščenko, Vadim S. 1943- Dynamical chaos - basic concepts Teubner-Texte zur Physik Chaotic behavior in systems Differentiable dynamical systems Chaotisches System (DE-588)4316104-2 gnd Chaos (DE-588)4191419-3 gnd Chaostheorie (DE-588)4009754-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4316104-2 (DE-588)4191419-3 (DE-588)4009754-7 (DE-588)4013396-5 |
| title | Dynamical chaos - basic concepts |
| title_auth | Dynamical chaos - basic concepts |
| title_exact_search | Dynamical chaos - basic concepts |
| title_full | Dynamical chaos - basic concepts V. S. Anishchenko |
| title_fullStr | Dynamical chaos - basic concepts V. S. Anishchenko |
| title_full_unstemmed | Dynamical chaos - basic concepts V. S. Anishchenko |
| title_short | Dynamical chaos - basic concepts |
| title_sort | dynamical chaos basic concepts |
| topic | Chaotic behavior in systems Differentiable dynamical systems Chaotisches System (DE-588)4316104-2 gnd Chaos (DE-588)4191419-3 gnd Chaostheorie (DE-588)4009754-7 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Chaotic behavior in systems Differentiable dynamical systems Chaotisches System Chaos Chaostheorie Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001399554&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000019271 |
| work_keys_str_mv | AT aniscenkovadims dynamicalchaosbasicconcepts |