内容提要 《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。 目录 PrefaceChapter 1 Linear Systems and Stab1.1 Linear systems with distinct eigenvalues1.2 Operator exponentials1.3 Linear systems with repeated eigenvalues1.4 Nonhomogeneous linear systems1.5 Linear systems with periodic coefficients1.6 Stability and boundary1.7 Lower-dimensional linear systems1.7.1 One-dimensional linear systems1.7.2 Planar linear systems1.7.3 Three-dimensional linear systemsReferencesChapter 2 Stability Switching and Bifurcatio2.1 Continuous dynamical systems2.2 Equilibriums and stabilit2.3 Bifurcation and stability switching2.3.1 Stability and switching2.3.2 Bifurcations2.3.3 Lyapunov functions and stabilityReferencesChapter 3 Analytical Periodic Flows and Chaos3.1 Analytical periodic flows3.1.1 Autonomous nonlinear systems3.1.2 Periodically forced nonlinear systems3.2 Nonlinear vibration systems3.2.1 Free vibration systems3.2.2 Periodically forced vibration systems3.3 A periodically forced Duffing oscillatorReferencesChapter 4 Global Transversality and Chaos4.1 Nonlinear dynamical systems4.2 Local and global flows4.3 Global transversal4.4 Global tangency4.5 Perturbed Hamiltonian systems4.6 Two-dimensional Hamiltonian systems4.7 First integral quantity increment4.8 A damped Duffing oscillator4.8.1 Conditions for global transversality and tangency4.8.2 Poincare mapping and mapping structures4.8.3 Bifurcation scenario4.8.4 NumericalillustrationsReferencesChapter 5 Resonance and Hamiltonian Chaos5.1 Stochastic layers5.1.1 Definitions5.1.2 Appromate criteria5.2 Resonant separatrix layers5.2.1 Layer dynamics5.2.2 Appromate criteria5.3 A periodically forced Duffing oscillator5.3.1 Appromate predictions5.3.2 Numericalillustrations5.4 Concluding remarksReferencesIndex 作者介绍
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