Strange nonchaotic attractors :: dynamics between order and chaos in quasiperiodically forced systems /
This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of S...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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New Jersey :
World Scientific,
©2006.
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| Schriftenreihe: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 56. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov. |
| Beschreibung: | 1 online resource (xi, 213 pages :) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789812774408 9812774408 1281919454 9781281919458 9786611919450 6611919457 |
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| 245 | 1 | 0 | |a Strange nonchaotic attractors : |b dynamics between order and chaos in quasiperiodically forced systems / |c Ulrike Feudel, Sergey Kuznetsov, Arkady Pikovsky. |
| 260 | |a New Jersey : |b World Scientific, |c ©2006. | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a 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. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Attractors (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh97005887 | |
| 650 | 0 | |a Chaotic behavior in systems. |0 http://id.loc.gov/authorities/subjects/sh85022562 | |
| 650 | 0 | |a Differentiable dynamical systems. |0 http://id.loc.gov/authorities/subjects/sh85037882 | |
| 650 | 0 | |a Nonlinear systems. |0 http://id.loc.gov/authorities/subjects/sh96001350 | |
| 650 | 6 | |a Attracteurs (Mathématiques) | |
| 650 | 6 | |a Chaos. | |
| 650 | 6 | |a Dynamique différentiable. | |
| 650 | 6 | |a Systèmes non linéaires. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Attractors (Mathematics) |2 fast | |
| 650 | 7 | |a Chaotic behavior in systems |2 fast | |
| 650 | 7 | |a Differentiable dynamical systems |2 fast | |
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| 700 | 1 | |a Kuznet︠s︡ov, S. P. |q (Sergeĭ Petrovich), |d 1951- |1 https://id.oclc.org/worldcat/entity/E39PCjrCCrT3p8R9MF3TrGtPYq | |
| 700 | 1 | |a Pikovsky, Arkady, |d 1956- |1 https://id.oclc.org/worldcat/entity/E39PBJdGGHXYHQ7xPqJbTXYMfq |0 http://id.loc.gov/authorities/names/n2001002204 | |
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| 776 | 0 | 8 | |i Print version: |a Feudel, Ulrike. |t Strange nonchaotic attractors. |d New Jersey : World Scientific, ©2006 |w (DLC) 2006283584 |
| 830 | 0 | |a World Scientific series on nonlinear science. |n Series A, |p Monographs and treatises ; |v v. 56. |0 http://id.loc.gov/authorities/names/no94008495 | |
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| contents | 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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| discipline | Mathematik |
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| id | ZDB-4-EBA-ocn299585066 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:17:00Z |
| institution | BVB |
| isbn | 9789812774408 9812774408 1281919454 9781281919458 9786611919450 6611919457 |
| language | English |
| lccn | 2006283584 |
| oclc_num | 299585066 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xi, 213 pages :) |
| psigel | ZDB-4-EBA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | World Scientific, |
| record_format | marc |
| series | World Scientific series on nonlinear science. Monographs and treatises ; |
| series2 | World Scientific series on nonlinear science. Series A, Monographs and treatises ; |
| spelling | Feudel, Ulrike. http://id.loc.gov/authorities/names/nb2006016030 Strange nonchaotic attractors : dynamics between order and chaos in quasiperiodically forced systems / Ulrike Feudel, Sergey Kuznetsov, Arkady Pikovsky. New Jersey : World Scientific, ©2006. 1 online resource (xi, 213 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier World Scientific series on nonlinear science. Series A, Monographs and treatises ; 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. Print version record. This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov. English. Attractors (Mathematics) http://id.loc.gov/authorities/subjects/sh97005887 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Differentiable dynamical systems. http://id.loc.gov/authorities/subjects/sh85037882 Nonlinear systems. http://id.loc.gov/authorities/subjects/sh96001350 Attracteurs (Mathématiques) Chaos. Dynamique différentiable. Systèmes non linéaires. MATHEMATICS Differential Equations General. bisacsh Attractors (Mathematics) fast Chaotic behavior in systems fast Differentiable dynamical systems fast Nonlinear systems fast Kuznet︠s︡ov, S. P. (Sergeĭ Petrovich), 1951- https://id.oclc.org/worldcat/entity/E39PCjrCCrT3p8R9MF3TrGtPYq Pikovsky, Arkady, 1956- https://id.oclc.org/worldcat/entity/E39PBJdGGHXYHQ7xPqJbTXYMfq http://id.loc.gov/authorities/names/n2001002204 has work: Strange nonchaotic attractors (Text) https://id.oclc.org/worldcat/entity/E39PCGF7vv8gQFjBkYtyXhg4tq https://id.oclc.org/worldcat/ontology/hasWork Print version: Feudel, Ulrike. Strange nonchaotic attractors. New Jersey : World Scientific, ©2006 (DLC) 2006283584 World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 56. http://id.loc.gov/authorities/names/no94008495 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210547 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210547 Volltext |
| spellingShingle | Feudel, Ulrike Strange nonchaotic attractors : dynamics between order and chaos in quasiperiodically forced systems / World Scientific series on nonlinear science. Monographs and treatises ; 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. Attractors (Mathematics) http://id.loc.gov/authorities/subjects/sh97005887 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Differentiable dynamical systems. http://id.loc.gov/authorities/subjects/sh85037882 Nonlinear systems. http://id.loc.gov/authorities/subjects/sh96001350 Attracteurs (Mathématiques) Chaos. Dynamique différentiable. Systèmes non linéaires. MATHEMATICS Differential Equations General. bisacsh Attractors (Mathematics) fast Chaotic behavior in systems fast Differentiable dynamical systems fast Nonlinear systems fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh97005887 http://id.loc.gov/authorities/subjects/sh85022562 http://id.loc.gov/authorities/subjects/sh85037882 http://id.loc.gov/authorities/subjects/sh96001350 |
| 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 | Attractors (Mathematics) http://id.loc.gov/authorities/subjects/sh97005887 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Differentiable dynamical systems. http://id.loc.gov/authorities/subjects/sh85037882 Nonlinear systems. http://id.loc.gov/authorities/subjects/sh96001350 Attracteurs (Mathématiques) Chaos. Dynamique différentiable. Systèmes non linéaires. MATHEMATICS Differential Equations General. bisacsh Attractors (Mathematics) fast Chaotic behavior in systems fast Differentiable dynamical systems fast Nonlinear systems fast |
| topic_facet | Attractors (Mathematics) Chaotic behavior in systems. Differentiable dynamical systems. Nonlinear systems. Attracteurs (Mathématiques) Chaos. Dynamique différentiable. Systèmes non linéaires. MATHEMATICS Differential Equations General. Chaotic behavior in systems Differentiable dynamical systems Nonlinear systems |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210547 |
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