《非线性物理科学：离散和切换动力系统（英文版）》用一种清晰简明、独特的观点讨论非线性离散动力系统稳定性和分叉理论，并分析了离散动力系统中稳定性及其切换的复杂性。本书首先介绍了含多重特征根的线性离散系统的解析解和稳定性理论，给出了详细的离散非线性动力系统的稳定性和奇异性分类；然后通过众多例子展示离散动力系统中的混沌及其分形性，并应用正映射和负映射讨论了非线性离散动力系统完整动力学，包括其不动点和混沌的阴阳解。本书还系统地讨论了具有搬运跳跃律的切换系统稳定性，将其作为描述连续和离散混合系统最一般的形式；并介绍了一种广义的符号动力学——映射动力学，通过此动力学讨论在边界不连续动力系统的擦边分叉以及奇异吸引子碎裂机理，以帮助读者更好地理解离散、切换不连续和边界不连续动力系统中的规则性和复杂性。
本书可作为应用数学、物理、工程学、经济动力学和金融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 Discrete Systems and Stability
- 1.1 Basic iterative solutions
- 1.2 Linear discrete systems with distinct eigenvalues
- 1.3 Linear discrete systems with repeated eigenvalues
- 1.4 Stability and boundary
- 1.5 Lower-dimensional discrete systems
- 1.5.1 One-dimensional systems
- 1.5.2 Planar discrete linear systems
- 1.5.3 Three-dimensional discrete systems
- Reference
- Chapter 2 Stability, Bifurcation and Routes to Chaos
- 2.1 Discrete dynamical systems
- 2.2 Fixed points and stability
- 2.3 Bifurcation and stability switching
- 2.3.1 Stability and switching
- 2.3.2 Bifurcations
- 2.4 Routes to chaos
- 2.4.1 One-dimensional maps
- 2.4.2 Two-dimensional maps
- References
- Chapter 3 Fractality and Complete Dynamics
- 3.1 Multifractals in 1-D iterative maps
- 3.1.1 Similar structures in period doubling
- 3.1.2 Fractality of chaos via period doubling bifurcations
- 3.1.3 An example
- 3.2 Bouncing ball dynamics
- 3.2.1 Periodic motions
- 3.2.2 Stability and bifurcations
- 3.2.3 Numerical illustrations
- 3.3 Positive and negative dynamics of discrete systems
- 3.4 Complete dynamics of Henon map
- References
- Chapter 4 Switching Systems with Transports
- 4.1 Continuous subsystems
- 4.2 Switching systems
- 4.3 Measuring functions and stability
- 4.4 Mappings and periodic flows
- 4.5 Linear switching systems
- 4.5.1 Vibrations with piecewise forces
- 4.5.2 Vector fields switching
- References
- Chapter 5 Mapping Dynamics and Fragmentation
- 5.1 Discontinuous dynamical systems
- 5.2 G-functions to boundaries
- 5.3 Mapping dynamics
- 5.4 A semi-active suspension system
- 5.4.1 Analytical dynamics
- 5.4.2 Illustrations
- 5.5 Grazing singular sets and fragmentation
- 5.6 Fragmentized strange attractors
- References
