Global transversality, resonance and chaotic dynamics /:
This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
©2008.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics. |
| Beschreibung: | 1 online resource (xii, 447 pages) : illustrations (some color) |
| Bibliographie: | Includes bibliographical references (pages 437-444) and index. |
| ISBN: | 9789812771124 9812771123 1281911682 9781281911681 9786611911683 6611911685 |
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| 245 | 1 | 0 | |a Global transversality, resonance and chaotic dynamics / |c Albert C.J. Luo. |
| 260 | |a Singapore ; |a Hackensack, NJ : |b World Scientific, |c ©2008. | ||
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| 504 | |a Includes bibliographical references (pages 437-444) and index. | ||
| 505 | 0 | |a Ch. 1. Introduction. 1.1. A brief history of dynamics. 1.2. Nonlinear Hamiltonian systems. 1.3. Dissipative nonlinear systems. 1.4. Book layout -- ch. 2. Differential geometry of flows. 2.1. Normal distance and G-functions. 2.2. Non-contact flows. 2.3. Contact flows. 2.4. Concluding remarks -- ch. 3. Global transversality in continuous dynamical systems. 3.1. Nonlinear dynamical systems. 3.2. Local and global flows. 3.3. Global transversality. 3.4. Global tangency. 3.5. Perturbed Hamiltonian systems. 3.6. Two-dimensional Hamiltonian systems. 3.7. A damped Duffing oscillator. 3.8. Global transversality to a generalized separatrix -- ch. 4. Chaotic layer dynamics. 4.1. Chaotic domains in phase space. 4.2. First integral quantity increments. 4.3. Resonance mechanism of chaotic layers. 4.4. Energy increments in perturbed Hamiltonian systems -- ch. 5. Two-dimensional stochastic layers. 5.1. Geometric description in phase space. 5.2. Approximate predictions. 5.3. Stochastic layer in a Duffing oscillator. 5.4. Conclusions and discussions -- ch. 6. Stochasticity in resonant separatrix layers. 6.1. Two-dimensional resonant separatrix layers. 6.2. 2n-dimensional resonant separatrix layers. 6.3. Resonant layers in a Duffing oscillator. 6.4. Resonant layers in a parametric pendulum -- ch. 7. Nonlinear dynamics on an equi-energy surface. 7.1. Hamiltonian systems. 7.2. Nonlinear resonance. 7.3. Energy spectrum. 7.4. Chaotic motions on an equi-energy surface. 7.5. Conclusions -- ch. 8. Stability and grazing in dissipative systems. 8.1. Equilibrium stability. 8.2. Periodic flow stability. 8.3. Local grazing bifurcation. 8.4. Global grazing bifurcation -- ch. 9. Global dynamics in two-dimensional dynamical systems. 9.1. Tangency and transversality. 9.2. Energy increment and Melnikov function. 9.3. Mapping structures. 9.4. Bifurcation scenario. 9.5. Numerical illustrations -- ch. 10. Flow switchability in discontinuous dynamical systems. 10.1. Discontinuous dynamical systems. 10.2. Passable flows. 10.3. Non-passable flows. 10.4. Tangential flows. 10.5. Flow switching bifurcations. 10.6. First integral quantity increment. | |
| 520 | |a This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics. | ||
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| contents | Ch. 1. Introduction. 1.1. A brief history of dynamics. 1.2. Nonlinear Hamiltonian systems. 1.3. Dissipative nonlinear systems. 1.4. Book layout -- ch. 2. Differential geometry of flows. 2.1. Normal distance and G-functions. 2.2. Non-contact flows. 2.3. Contact flows. 2.4. Concluding remarks -- ch. 3. Global transversality in continuous dynamical systems. 3.1. Nonlinear dynamical systems. 3.2. Local and global flows. 3.3. Global transversality. 3.4. Global tangency. 3.5. Perturbed Hamiltonian systems. 3.6. Two-dimensional Hamiltonian systems. 3.7. A damped Duffing oscillator. 3.8. Global transversality to a generalized separatrix -- ch. 4. Chaotic layer dynamics. 4.1. Chaotic domains in phase space. 4.2. First integral quantity increments. 4.3. Resonance mechanism of chaotic layers. 4.4. Energy increments in perturbed Hamiltonian systems -- ch. 5. Two-dimensional stochastic layers. 5.1. Geometric description in phase space. 5.2. Approximate predictions. 5.3. Stochastic layer in a Duffing oscillator. 5.4. Conclusions and discussions -- ch. 6. Stochasticity in resonant separatrix layers. 6.1. Two-dimensional resonant separatrix layers. 6.2. 2n-dimensional resonant separatrix layers. 6.3. Resonant layers in a Duffing oscillator. 6.4. Resonant layers in a parametric pendulum -- ch. 7. Nonlinear dynamics on an equi-energy surface. 7.1. Hamiltonian systems. 7.2. Nonlinear resonance. 7.3. Energy spectrum. 7.4. Chaotic motions on an equi-energy surface. 7.5. Conclusions -- ch. 8. Stability and grazing in dissipative systems. 8.1. Equilibrium stability. 8.2. Periodic flow stability. 8.3. Local grazing bifurcation. 8.4. Global grazing bifurcation -- ch. 9. Global dynamics in two-dimensional dynamical systems. 9.1. Tangency and transversality. 9.2. Energy increment and Melnikov function. 9.3. Mapping structures. 9.4. Bifurcation scenario. 9.5. Numerical illustrations -- ch. 10. Flow switchability in discontinuous dynamical systems. 10.1. Discontinuous dynamical systems. 10.2. Passable flows. 10.3. Non-passable flows. 10.4. Tangential flows. 10.5. Flow switching bifurcations. 10.6. First integral quantity increment. |
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| dewey-search | 003/.857 |
| dewey-sort | 13 3857 |
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| discipline | Informatik |
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Introduction. 1.1. A brief history of dynamics. 1.2. Nonlinear Hamiltonian systems. 1.3. Dissipative nonlinear systems. 1.4. Book layout -- ch. 2. Differential geometry of flows. 2.1. Normal distance and G-functions. 2.2. Non-contact flows. 2.3. Contact flows. 2.4. Concluding remarks -- ch. 3. Global transversality in continuous dynamical systems. 3.1. Nonlinear dynamical systems. 3.2. Local and global flows. 3.3. Global transversality. 3.4. Global tangency. 3.5. Perturbed Hamiltonian systems. 3.6. Two-dimensional Hamiltonian systems. 3.7. A damped Duffing oscillator. 3.8. Global transversality to a generalized separatrix -- ch. 4. Chaotic layer dynamics. 4.1. Chaotic domains in phase space. 4.2. First integral quantity increments. 4.3. Resonance mechanism of chaotic layers. 4.4. Energy increments in perturbed Hamiltonian systems -- ch. 5. Two-dimensional stochastic layers. 5.1. Geometric description in phase space. 5.2. Approximate predictions. 5.3. Stochastic layer in a Duffing oscillator. 5.4. Conclusions and discussions -- ch. 6. Stochasticity in resonant separatrix layers. 6.1. Two-dimensional resonant separatrix layers. 6.2. 2n-dimensional resonant separatrix layers. 6.3. Resonant layers in a Duffing oscillator. 6.4. Resonant layers in a parametric pendulum -- ch. 7. Nonlinear dynamics on an equi-energy surface. 7.1. Hamiltonian systems. 7.2. Nonlinear resonance. 7.3. Energy spectrum. 7.4. Chaotic motions on an equi-energy surface. 7.5. Conclusions -- ch. 8. Stability and grazing in dissipative systems. 8.1. Equilibrium stability. 8.2. Periodic flow stability. 8.3. Local grazing bifurcation. 8.4. Global grazing bifurcation -- ch. 9. Global dynamics in two-dimensional dynamical systems. 9.1. Tangency and transversality. 9.2. Energy increment and Melnikov function. 9.3. Mapping structures. 9.4. Bifurcation scenario. 9.5. Numerical illustrations -- ch. 10. Flow switchability in discontinuous dynamical systems. 10.1. 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| id | ZDB-4-EBA-ocn262540316 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:32Z |
| institution | BVB |
| isbn | 9789812771124 9812771123 1281911682 9781281911681 9786611911683 6611911685 |
| language | English |
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| publisher | World Scientific, |
| record_format | marc |
| spelling | Luo, Albert C. J. http://id.loc.gov/authorities/names/no99008309 Global transversality, resonance and chaotic dynamics / Albert C.J. Luo. Singapore ; Hackensack, NJ : World Scientific, ©2008. 1 online resource (xii, 447 pages) : illustrations (some color) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 437-444) and index. Ch. 1. Introduction. 1.1. A brief history of dynamics. 1.2. Nonlinear Hamiltonian systems. 1.3. Dissipative nonlinear systems. 1.4. Book layout -- ch. 2. Differential geometry of flows. 2.1. Normal distance and G-functions. 2.2. Non-contact flows. 2.3. Contact flows. 2.4. Concluding remarks -- ch. 3. Global transversality in continuous dynamical systems. 3.1. Nonlinear dynamical systems. 3.2. Local and global flows. 3.3. Global transversality. 3.4. Global tangency. 3.5. Perturbed Hamiltonian systems. 3.6. Two-dimensional Hamiltonian systems. 3.7. A damped Duffing oscillator. 3.8. Global transversality to a generalized separatrix -- ch. 4. Chaotic layer dynamics. 4.1. Chaotic domains in phase space. 4.2. First integral quantity increments. 4.3. Resonance mechanism of chaotic layers. 4.4. Energy increments in perturbed Hamiltonian systems -- ch. 5. Two-dimensional stochastic layers. 5.1. Geometric description in phase space. 5.2. Approximate predictions. 5.3. Stochastic layer in a Duffing oscillator. 5.4. Conclusions and discussions -- ch. 6. Stochasticity in resonant separatrix layers. 6.1. Two-dimensional resonant separatrix layers. 6.2. 2n-dimensional resonant separatrix layers. 6.3. Resonant layers in a Duffing oscillator. 6.4. Resonant layers in a parametric pendulum -- ch. 7. Nonlinear dynamics on an equi-energy surface. 7.1. Hamiltonian systems. 7.2. Nonlinear resonance. 7.3. Energy spectrum. 7.4. Chaotic motions on an equi-energy surface. 7.5. Conclusions -- ch. 8. Stability and grazing in dissipative systems. 8.1. Equilibrium stability. 8.2. Periodic flow stability. 8.3. Local grazing bifurcation. 8.4. Global grazing bifurcation -- ch. 9. Global dynamics in two-dimensional dynamical systems. 9.1. Tangency and transversality. 9.2. Energy increment and Melnikov function. 9.3. Mapping structures. 9.4. Bifurcation scenario. 9.5. Numerical illustrations -- ch. 10. Flow switchability in discontinuous dynamical systems. 10.1. Discontinuous dynamical systems. 10.2. Passable flows. 10.3. Non-passable flows. 10.4. Tangential flows. 10.5. Flow switching bifurcations. 10.6. First integral quantity increment. This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics. Print version record. English. Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Nonlinear systems. http://id.loc.gov/authorities/subjects/sh96001350 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Dynamique. Systèmes non linéaires. Chaos. kinetics (dynamics) aat SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Dynamics fast Nonlinear systems fast Print version: Luo, Albert C.J. Global transversality, resonance and chaotic dynamics. Singapore ; Hackensack, NJ : World Scientific, ©2008 9812771115 9789812771117 (DLC) 2008299311 (OCoLC)173808086 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=236069 Volltext |
| spellingShingle | Luo, Albert C. J. Global transversality, resonance and chaotic dynamics / Ch. 1. Introduction. 1.1. A brief history of dynamics. 1.2. Nonlinear Hamiltonian systems. 1.3. Dissipative nonlinear systems. 1.4. Book layout -- ch. 2. Differential geometry of flows. 2.1. Normal distance and G-functions. 2.2. Non-contact flows. 2.3. Contact flows. 2.4. Concluding remarks -- ch. 3. Global transversality in continuous dynamical systems. 3.1. Nonlinear dynamical systems. 3.2. Local and global flows. 3.3. Global transversality. 3.4. Global tangency. 3.5. Perturbed Hamiltonian systems. 3.6. Two-dimensional Hamiltonian systems. 3.7. A damped Duffing oscillator. 3.8. Global transversality to a generalized separatrix -- ch. 4. Chaotic layer dynamics. 4.1. Chaotic domains in phase space. 4.2. First integral quantity increments. 4.3. Resonance mechanism of chaotic layers. 4.4. Energy increments in perturbed Hamiltonian systems -- ch. 5. Two-dimensional stochastic layers. 5.1. Geometric description in phase space. 5.2. Approximate predictions. 5.3. Stochastic layer in a Duffing oscillator. 5.4. Conclusions and discussions -- ch. 6. Stochasticity in resonant separatrix layers. 6.1. Two-dimensional resonant separatrix layers. 6.2. 2n-dimensional resonant separatrix layers. 6.3. Resonant layers in a Duffing oscillator. 6.4. Resonant layers in a parametric pendulum -- ch. 7. Nonlinear dynamics on an equi-energy surface. 7.1. Hamiltonian systems. 7.2. Nonlinear resonance. 7.3. Energy spectrum. 7.4. Chaotic motions on an equi-energy surface. 7.5. Conclusions -- ch. 8. Stability and grazing in dissipative systems. 8.1. Equilibrium stability. 8.2. Periodic flow stability. 8.3. Local grazing bifurcation. 8.4. Global grazing bifurcation -- ch. 9. Global dynamics in two-dimensional dynamical systems. 9.1. Tangency and transversality. 9.2. Energy increment and Melnikov function. 9.3. Mapping structures. 9.4. Bifurcation scenario. 9.5. Numerical illustrations -- ch. 10. Flow switchability in discontinuous dynamical systems. 10.1. Discontinuous dynamical systems. 10.2. Passable flows. 10.3. Non-passable flows. 10.4. Tangential flows. 10.5. Flow switching bifurcations. 10.6. First integral quantity increment. Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Nonlinear systems. http://id.loc.gov/authorities/subjects/sh96001350 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Dynamique. Systèmes non linéaires. Chaos. kinetics (dynamics) aat SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Dynamics fast Nonlinear systems fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85040316 http://id.loc.gov/authorities/subjects/sh96001350 http://id.loc.gov/authorities/subjects/sh85022562 |
| title | Global transversality, resonance and chaotic dynamics / |
| title_auth | Global transversality, resonance and chaotic dynamics / |
| title_exact_search | Global transversality, resonance and chaotic dynamics / |
| title_full | Global transversality, resonance and chaotic dynamics / Albert C.J. Luo. |
| title_fullStr | Global transversality, resonance and chaotic dynamics / Albert C.J. Luo. |
| title_full_unstemmed | Global transversality, resonance and chaotic dynamics / Albert C.J. Luo. |
| title_short | Global transversality, resonance and chaotic dynamics / |
| title_sort | global transversality resonance and chaotic dynamics |
| topic | Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Nonlinear systems. http://id.loc.gov/authorities/subjects/sh96001350 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Dynamique. Systèmes non linéaires. Chaos. kinetics (dynamics) aat SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Dynamics fast Nonlinear systems fast |
| topic_facet | Dynamics. Nonlinear systems. Chaotic behavior in systems. Dynamique. Systèmes non linéaires. Chaos. kinetics (dynamics) SCIENCE Chaotic Behavior in Systems. Chaotic behavior in systems Dynamics Nonlinear systems |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=236069 |
| work_keys_str_mv | AT luoalbertcj globaltransversalityresonanceandchaoticdynamics |