An introduction to dynamical systems and chaos:
This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes to chaos and multistable c...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore
Springer
[2024]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | University texts in the mathematical sciences
|
| Schlagworte: | |
| Zusammenfassung: | This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes to chaos and multistable coexisting attractors. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, featuring a multitude of detailed worked-out examples alongside comprehensive exercises. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate, graduate and research students in mathematics, physics and engineering. The second edition of the book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillations, Bogdanov–Takens, periodbubbling and Neimark–Sacker bifurcations, and dynamics on circle. The organized structures in bi-parameter plane for transitional and chaotic regimes are new active research interest and explored thoroughly. The connections of complex chaotic attractors with fractals cascades are explored in many physical systems. Chaotic attractors may attain multiple scaling factors and show scale invariance property. Finally, the ideas of multifractals and global spectrum for quantifying inhomogeneous chaotic attractors are discussed |
| Beschreibung: | This book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems, and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and several examples are worked out in detail and exercises have been included. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate and graduate students in mathematics, physics, and engineering. The second edition of the book includes a new chapter on Reynold and Kolmogrov turbulence. The entire book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillation, pitchfork bifurcation, transcritical bifurcation, Bogdonov–Takens bifurcation, canonical invariant and symmetry properties, turbulent planar plume flow, and dynamics on circle, organized structure in chaos and multifractals 1. Continuous Dynamical Systems.- 2. Linear Systems.- 3. Phase Plane Analysis.- 4. Stability Theory.- 5. Oscillation.- 6. Theory of Bifurcations.- 7. Hamiltonian Systems.- 8. Symmetry Analysis.- 9. Discrete Dynamical Systems.- 10. Some maps.- 11. Conjugacy Maps.- 12. Chaos.- 13. Fractals.- 14. Turbulence: Reynolds to Kolmogrov and Beyond.- Index. |
| Beschreibung: | xvii, 688 Seiten Illustrationen, Diagramme 235 mm |
| ISBN: | 9789819976942 9789819976973 |
Internformat
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| 500 | |a This book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems, and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and several examples are worked out in detail and exercises have been included. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate and graduate students in mathematics, physics, and engineering. The second edition of the book includes a new chapter on Reynold and Kolmogrov turbulence. The entire book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillation, pitchfork bifurcation, transcritical bifurcation, Bogdonov–Takens bifurcation, canonical invariant and symmetry properties, turbulent planar plume flow, and dynamics on circle, organized structure in chaos and multifractals | ||
| 500 | |a 1. Continuous Dynamical Systems.- 2. Linear Systems.- 3. Phase Plane Analysis.- 4. Stability Theory.- 5. Oscillation.- 6. Theory of Bifurcations.- 7. Hamiltonian Systems.- 8. Symmetry Analysis.- 9. Discrete Dynamical Systems.- 10. Some maps.- 11. Conjugacy Maps.- 12. Chaos.- 13. Fractals.- 14. Turbulence: Reynolds to Kolmogrov and Beyond.- Index. | ||
| 520 | |a This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes to chaos and multistable coexisting attractors. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, featuring a multitude of detailed worked-out examples alongside comprehensive exercises. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate, graduate and research students in mathematics, physics and engineering. The second edition of the book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillations, Bogdanov–Takens, periodbubbling and Neimark–Sacker bifurcations, and dynamics on circle. The organized structures in bi-parameter plane for transitional and chaotic regimes are new active research interest and explored thoroughly. The connections of complex chaotic attractors with fractals cascades are explored in many physical systems. Chaotic attractors may attain multiple scaling factors and show scale invariance property. Finally, the ideas of multifractals and global spectrum for quantifying inhomogeneous chaotic attractors are discussed | ||
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Datensatz im Suchindex
| _version_ | 1805083847745863680 |
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| author | Layek, G. C. |
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| id | DE-604.BV049679175 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:55:04Z |
| institution | BVB |
| isbn | 9789819976942 9789819976973 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035021995 |
| oclc_num | 1422191139 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | xvii, 688 Seiten Illustrationen, Diagramme 235 mm |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Springer |
| record_format | marc |
| series2 | University texts in the mathematical sciences |
| spelling | Layek, G. C. Verfasser (DE-588)1088578667 aut An introduction to dynamical systems and chaos G.C. Layek Second edition Singapore Springer [2024] xvii, 688 Seiten Illustrationen, Diagramme 235 mm txt rdacontent n rdamedia nc rdacarrier University texts in the mathematical sciences This book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems, and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and several examples are worked out in detail and exercises have been included. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate and graduate students in mathematics, physics, and engineering. The second edition of the book includes a new chapter on Reynold and Kolmogrov turbulence. The entire book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillation, pitchfork bifurcation, transcritical bifurcation, Bogdonov–Takens bifurcation, canonical invariant and symmetry properties, turbulent planar plume flow, and dynamics on circle, organized structure in chaos and multifractals 1. Continuous Dynamical Systems.- 2. Linear Systems.- 3. Phase Plane Analysis.- 4. Stability Theory.- 5. Oscillation.- 6. Theory of Bifurcations.- 7. Hamiltonian Systems.- 8. Symmetry Analysis.- 9. Discrete Dynamical Systems.- 10. Some maps.- 11. Conjugacy Maps.- 12. Chaos.- 13. Fractals.- 14. Turbulence: Reynolds to Kolmogrov and Beyond.- Index. This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes to chaos and multistable coexisting attractors. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, featuring a multitude of detailed worked-out examples alongside comprehensive exercises. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate, graduate and research students in mathematics, physics and engineering. The second edition of the book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillations, Bogdanov–Takens, periodbubbling and Neimark–Sacker bifurcations, and dynamics on circle. The organized structures in bi-parameter plane for transitional and chaotic regimes are new active research interest and explored thoroughly. The connections of complex chaotic attractors with fractals cascades are explored in many physical systems. Chaotic attractors may attain multiple scaling factors and show scale invariance property. Finally, the ideas of multifractals and global spectrum for quantifying inhomogeneous chaotic attractors are discussed bisacsh Dynamical systems Dynamisches System (DE-588)4013396-5 gnd rswk-swf Chaostheorie (DE-588)4009754-7 gnd rswk-swf Hardcover, Softcover / Mathematik/Analysis Dynamisches System (DE-588)4013396-5 s Chaostheorie (DE-588)4009754-7 s DE-604 Erscheint auch als Online-Ausgabe 978-981-99-7695-9 |
| spellingShingle | Layek, G. C. An introduction to dynamical systems and chaos bisacsh Dynamical systems Dynamisches System (DE-588)4013396-5 gnd Chaostheorie (DE-588)4009754-7 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4009754-7 |
| title | An introduction to dynamical systems and chaos |
| title_auth | An introduction to dynamical systems and chaos |
| title_exact_search | An introduction to dynamical systems and chaos |
| title_full | An introduction to dynamical systems and chaos G.C. Layek |
| title_fullStr | An introduction to dynamical systems and chaos G.C. Layek |
| title_full_unstemmed | An introduction to dynamical systems and chaos G.C. Layek |
| title_short | An introduction to dynamical systems and chaos |
| title_sort | an introduction to dynamical systems and chaos |
| topic | bisacsh Dynamical systems Dynamisches System (DE-588)4013396-5 gnd Chaostheorie (DE-588)4009754-7 gnd |
| topic_facet | bisacsh Dynamical systems Dynamisches System Chaostheorie |
| work_keys_str_mv | AT layekgc anintroductiontodynamicalsystemsandchaos |