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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ :
World Scientific,
©2008.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.