Strange nonchaotic attractors: dynamics between order and chaos in quasiperiodically forced systems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
c2006
|
| Schriftenreihe: | World Scientific series on nonlinear science
v. 56 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and index 1. Introduction. 1.1. Periodicity and quasiperiodicity. 1.2. Robustness of quasiperiodic motions. 1.3. Strange nonchaotic attractors. 1.4. What is in the book -- 2. Models. 2.1. Differential equations and maps. 2.2. Quasiperiodically forced one-dimensional maps. 2.3. Quasiperiodically forced high-dimensional maps. 2.4. Quasiperiodically forced continuous-time systems. 2.5. Experiments. 2.6. Bibliographic notes -- 3. Rational approximations. 3.1. Properties of rational approximations of irrationals. 3.2. Rational approximations to quasiperiodic forcing. 3.3. Checking strangeness of SNA through rational approximations. 3.4. Bibliographic notes -- 4. Stability and instability. 4.1. Theoretical consideration. 4.2. Numerical examples. 4.3. Bibliographic notes -- 5. Fractal and statistical properties. 5.1. Fractal properties of SNA. 5.2. Correlations and spectra of SNA. 5.3. Bibliographic notes -- 6. Bifurcations in quasiperiodically forced systems and transitions to SNA. 6.1. Smooth and non-smooth bifurcations. 6.2. Bifurcations in the quasiperiodically forced logistic map. 6.3. Bifurcations in the quasiperiodically forced circle map. 6.4. Loss of transverse stability: blowout transition to SNA. 6.5. Intermittency. 6.6. Bibliographic notes -- 7. Renormalization group approach to the onset of SNA in maps with the golden-mean quasiperiodic driving. 7.1. Introduction: the main idea of the renormalization group analysis. 7.2. The basic functional equations for the golden-mean renormalization scheme. 7.3. A review of critical points. 7.4. RG analysis of the classic GM critical point. 7.5. RG analysis of the blowout birth of SNA. 7.6. RG analysis of the TDT critical point. 7.7. RG analysis of the TCT critical point. 7.8. RG analysis of the TF critical point. 7.9. Critical behavior in realistic systems. 7.10. Conclusion. 7.11. Bibliographic notes |
| Beschreibung: | 1 Online-Ressource (xi, 213 p.) |
| ISBN: | 9789812566331 9789812774408 9812566333 9812774408 |
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| 490 | 0 | |a World Scientific series on nonlinear science |v v. 56 | |
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Datensatz im Suchindex
| _version_ | 1804175460664344576 |
|---|---|
| any_adam_object | |
| author | Feudel, Ulrike |
| author_facet | Feudel, Ulrike |
| author_role | aut |
| author_sort | Feudel, Ulrike |
| author_variant | u f uf |
| building | Verbundindex |
| bvnumber | BV043074390 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.39 |
| dewey-search | 515/.39 |
| dewey-sort | 3515 239 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043074390 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:39Z |
| institution | BVB |
| isbn | 9789812566331 9789812774408 9812566333 9812774408 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028498582 |
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| publishDate | 2006 |
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| series2 | World Scientific series on nonlinear science |
| spelling | Feudel, Ulrike Verfasser aut Strange nonchaotic attractors dynamics between order and chaos in quasiperiodically forced systems Ulrike Feudel, Sergey Kuznetsov, Arkady Pikovsky New Jersey World Scientific c2006 1 Online-Ressource (xi, 213 p.) txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science v. 56 Includes bibliographical references and index 1. Introduction. 1.1. Periodicity and quasiperiodicity. 1.2. Robustness of quasiperiodic motions. 1.3. Strange nonchaotic attractors. 1.4. What is in the book -- 2. Models. 2.1. Differential equations and maps. 2.2. Quasiperiodically forced one-dimensional maps. 2.3. Quasiperiodically forced high-dimensional maps. 2.4. Quasiperiodically forced continuous-time systems. 2.5. Experiments. 2.6. Bibliographic notes -- 3. Rational approximations. 3.1. Properties of rational approximations of irrationals. 3.2. Rational approximations to quasiperiodic forcing. 3.3. Checking strangeness of SNA through rational approximations. 3.4. Bibliographic notes -- 4. Stability and instability. 4.1. Theoretical consideration. 4.2. Numerical examples. 4.3. Bibliographic notes -- 5. Fractal and statistical properties. 5.1. Fractal properties of SNA. 5.2. Correlations and spectra of SNA. 5.3. Bibliographic notes -- 6. Bifurcations in quasiperiodically forced systems and transitions to SNA. 6.1. Smooth and non-smooth bifurcations. 6.2. Bifurcations in the quasiperiodically forced logistic map. 6.3. Bifurcations in the quasiperiodically forced circle map. 6.4. Loss of transverse stability: blowout transition to SNA. 6.5. Intermittency. 6.6. Bibliographic notes -- 7. Renormalization group approach to the onset of SNA in maps with the golden-mean quasiperiodic driving. 7.1. Introduction: the main idea of the renormalization group analysis. 7.2. The basic functional equations for the golden-mean renormalization scheme. 7.3. A review of critical points. 7.4. RG analysis of the classic GM critical point. 7.5. RG analysis of the blowout birth of SNA. 7.6. RG analysis of the TDT critical point. 7.7. RG analysis of the TCT critical point. 7.8. RG analysis of the TF critical point. 7.9. Critical behavior in realistic systems. 7.10. Conclusion. 7.11. Bibliographic notes MATHEMATICS / Differential Equations / General bisacsh Attractors (Mathematics) fast Chaotic behavior in systems fast Differentiable dynamical systems fast Nonlinear systems fast Attractors (Mathematics) Chaotic behavior in systems Differentiable dynamical systems Nonlinear systems Attraktor (DE-588)4140563-8 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Attraktor (DE-588)4140563-8 s Chaotisches System (DE-588)4316104-2 s 1\p DE-604 Kuznetsov, Sergey Sonstige oth Pikovsky, Arkady Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=210547 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Feudel, Ulrike Strange nonchaotic attractors dynamics between order and chaos in quasiperiodically forced systems MATHEMATICS / Differential Equations / General bisacsh Attractors (Mathematics) fast Chaotic behavior in systems fast Differentiable dynamical systems fast Nonlinear systems fast Attractors (Mathematics) Chaotic behavior in systems Differentiable dynamical systems Nonlinear systems Attraktor (DE-588)4140563-8 gnd Chaotisches System (DE-588)4316104-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4140563-8 (DE-588)4316104-2 (DE-588)4137931-7 |
| title | Strange nonchaotic attractors dynamics between order and chaos in quasiperiodically forced systems |
| title_auth | Strange nonchaotic attractors dynamics between order and chaos in quasiperiodically forced systems |
| title_exact_search | Strange nonchaotic attractors dynamics between order and chaos in quasiperiodically forced systems |
| title_full | Strange nonchaotic attractors dynamics between order and chaos in quasiperiodically forced systems Ulrike Feudel, Sergey Kuznetsov, Arkady Pikovsky |
| title_fullStr | Strange nonchaotic attractors dynamics between order and chaos in quasiperiodically forced systems Ulrike Feudel, Sergey Kuznetsov, Arkady Pikovsky |
| title_full_unstemmed | Strange nonchaotic attractors dynamics between order and chaos in quasiperiodically forced systems Ulrike Feudel, Sergey Kuznetsov, Arkady Pikovsky |
| title_short | Strange nonchaotic attractors |
| title_sort | strange nonchaotic attractors dynamics between order and chaos in quasiperiodically forced systems |
| title_sub | dynamics between order and chaos in quasiperiodically forced systems |
| topic | MATHEMATICS / Differential Equations / General bisacsh Attractors (Mathematics) fast Chaotic behavior in systems fast Differentiable dynamical systems fast Nonlinear systems fast Attractors (Mathematics) Chaotic behavior in systems Differentiable dynamical systems Nonlinear systems Attraktor (DE-588)4140563-8 gnd Chaotisches System (DE-588)4316104-2 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | MATHEMATICS / Differential Equations / General Attractors (Mathematics) Chaotic behavior in systems Differentiable dynamical systems Nonlinear systems Attraktor Chaotisches System Differenzierbares dynamisches System |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=210547 |
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