Strange nonchaotic attractors : dynamics between order and chaos in quasiperiodically forced systems / Ulrike Feudel, Sergey Kuznetsov, Arkady Pikovsky.
Material type:
TextSeries: World Scientific series on nonlinear science. Series A, Monographs and treatises ; ; v. 56.Publication details: New Jersey : World Scientific, ©2006.Description: 1 online resource (xi, 213 pages) : illustrationsContent type: - text
- computer
- online resource
- 9789812774408
- 9812774408
- Attractors (Mathematics)
- Chaotic behavior in systems
- Differentiable dynamical systems
- Nonlinear systems
- Attracteurs (Mathématiques)
- Chaos
- Dynamique différentiable
- Systèmes non linéaires
- MATHEMATICS -- Differential Equations -- General
- Attractors (Mathematics)
- Chaotic behavior in systems
- Differentiable dynamical systems
- Nonlinear systems
- 515/.39 22
- QA614.813 .F48 2006eb
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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.
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