《非线性物理科学：连续动力系统（英文版）》极具创新特色，首次揭示了混沌不只是可以通过数字模拟实现，而且可以用解析形式来表示。书中提出了关于连续动力系统的稳定性和分叉理论的一种新的、清晰简明的观点，能够帮助读者更好地理解动力系统中的规则性和复杂性。本书首先介绍了含多重特征根的线性连续系统的解析解和稳定性理论，并详细讨论了非线性连续动力系统的稳定性和奇异性分类，然后系统地讨论动力系统从周期解到混沌的解析道路。此外本书还讨论了动力系统流对于同宿或异宿轨道分界面的全局横截性的解析预测并且给出了非线性哈密顿系统混沌的解析判据，从而能更好地确定混沌在非线性动力系统中的物理机理。
本书可作为应用数学、物理、力学和控制专业大学生的教材或参考书，也可供这些领域的教授和研究人员参考。
作者罗朝俊，非线性动力系统和力学领域国际知名专家，美国南伊利诺伊大学爱德华分校终身教授，主要研究领域为非线性哈密顿系统混沌、非线性力学和不连续动力系统。
- Preface
- Chapter 1 Linear Systems and Stab
- 1.1 Linear systems with distinct eigenvalues
- 1.2 Operator exponentials
- 1.3 Linear systems with repeated eigenvalues
- 1.4 Nonhomogeneous linear systems
- 1.5 Linear systems with periodic coefficients
- 1.6 Stability and boundary
- 1.7 Lower-dimensional linear systems
- 1.7.1 One-dimensional linear systems
- 1.7.2 Planar linear systems
- 1.7.3 Three-dimensional linear systems
- References
- Chapter 2 Stability Switching and Bifurcation
- 2.1 Continuous dynamical systems
- 2.2 Equilibriums and stabilit
- 2.3 Bifurcation and stability switching
- 2.3.1 Stability and switching
- 2.3.2 Bifurcations
- 2.3.3 Lyapunov functions and stability
- References
- Chapter 3 Analytical Periodic Flows and Chaos
- 3.1 Analytical periodic flows
- 3.1.1 Autonomous nonlinear systems
- 3.1.2 Periodically forced nonlinear systems
- 3.2 Nonlinear vibration systems
- 3.2.1 Free vibration systems
- 3.2.2 Periodically forced vibration systems
- 3.3 A periodically forced Duffing oscillator
- References
- Chapter 4 Global Transversality and Chaos
- 4.1 Nonlinear dynamical systems
- 4.2 Local and global flows
- 4.3 Global transversal
- 4.4 Global tangency
- 4.5 Perturbed Hamiltonian systems
- 4.6 Two-dimensional Hamiltonian systems
- 4.7 First integral quantity increment
- 4.8 A damped Duffing oscillator
- 4.8.1 Conditions for global transversality and tangency
- 4.8.2 Poincare mapping and mapping structures
- 4.8.3 Bifurcation scenario
- 4.8.4 Numericalillustrations
- References
- Chapter 5 Resonance and Hamiltonian Chaos
- 5.1 Stochastic layers
- 5.1.1 Definitions
- 5.1.2 Approximate criteria
- 5.2 Resonant separatrix layers
- 5.2.1 Layer dynamics
- 5.2.2 Approximate criteria
- 5.3 A periodically forced Duffing oscillator
- 5.3.1 Approximate predictions
- 5.3.2 Numericalillustrations
- 5.4 Concluding remarks
- References
